#' -----------------------------------------------------------------------------
#' Install the new version of the package
#' -----------------------------------------------------------------------------

#library(devtools)
#install_github("lvhoskovec/mmpack", build_vignettes = TRUE, force = TRUE)

library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──
## ✓ ggplot2 3.3.3     ✓ purrr   0.3.4
## ✓ tibble  3.0.6     ✓ dplyr   1.0.4
## ✓ tidyr   1.1.2     ✓ stringr 1.4.0
## ✓ readr   1.3.1     ✓ forcats 0.5.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library(lubridate)
## 
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union
library(haven)
library(readxl)
library(mmpack)

#' For ggplots
simple_theme <- theme(
  #aspect.ratio = 1,
  text  = element_text(family="Calibri",size = 12, color = 'black'),
  panel.spacing.y = unit(0,"cm"),
  panel.spacing.x = unit(0.25, "lines"),
  panel.grid.minor = element_line(color = "transparent"),
  panel.grid.major = element_line(color = "transparent"),
  panel.border=element_rect(fill = NA),
  panel.background=element_blank(),
  axis.ticks = element_line(colour = "black"),
  axis.text = element_text(color = "black", size=10),
  # legend.position = c(0.1,0.1),
  plot.margin=grid::unit(c(0,0,0,0), "mm"),
  legend.key = element_blank()
)
# windowsFonts(Calibri=windowsFont("TT Calibri"))
options(scipen = 9999) #avoid scientific notation

set.seed(123)

1 Sensitivty Analysis

In this version of the analysis, we are stratifying by race/ethnicity. This is the script for non-NHW participants. 05_NPB_Model_BW_v4b.Rmd has the script for all NHW participants

1.1 Exposure data

#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, mean_temp, pct_tree_cover, pct_impervious,
            mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
            cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
            pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
  as.matrix()
head(X)
##       mean_pm  mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 8.483046 47.19072  51.81487       6.006276       43.30893
## [2,] 6.598608 50.05090  58.32885       7.281109       48.36432
## [3,] 7.122537 50.14275  59.28421       3.357792       28.16745
## [4,] 7.637453 47.03125  55.32825      10.743612       45.87564
## [5,] 7.132364 48.46291  57.52274       5.166432       59.10860
## [6,] 7.245673 48.97393  56.14186       5.191274       26.88517
##      mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,]          10128.4962   2827.538   729.2371          4829.780
## [2,]          10749.0359   1576.420  5239.2211          4417.792
## [3,]            858.7283   2923.811  3427.2247          7006.042
## [4,]          15603.9800   3364.200  3166.5395          4484.960
## [5,]           4889.8576   2455.659  6164.1160          2206.505
## [6,]           2558.2207   3767.916  5762.0471          5376.856
##      dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,]          7968.654    29116.58        1749.1256     275.2480     155.7767
## [2,]          3780.951    51044.30        7354.5310     279.6435     226.8038
## [3,]          6806.912    29145.98         729.7784     194.1983     101.0046
## [4,]          5265.285    43921.85        5870.6867     174.3361     120.3281
## [5,]         11764.143    35210.72        3554.4858     293.6834     201.4526
## [6,]          6123.707    40422.63        5254.6965     286.1329     199.0948
##      violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,]          14.377133            37.32935   31.784946 11.529628
## [2,]           8.905404            67.03932   15.290231  4.908306
## [3,]           5.435988            22.49834   12.919186  5.234103
## [4,]           5.035971            47.15500    3.842365 10.000000
## [5,]          15.269587            55.92441   53.908629 27.461416
## [6,]          15.269587            55.92441   10.114247  8.240705
##      pct_limited_eng pct_hh_pov  pct_poc
## [1,]       26.114650  12.010919 90.33703
## [2,]        8.500401  18.123496 30.44025
## [3,]        6.307385   2.115768 73.60772
## [4,]        5.121799  25.171768 23.08698
## [5,]       37.742207  49.368155 91.67060
## [6,]        1.983365   9.149072 48.58072

Variance and histograms of the exposure variables (in their original units):

var(X)
##                           mean_pm       mean_o3     mean_temp pct_tree_cover
## mean_pm                0.40878878    0.01378123    0.05028648    -0.09908112
## mean_o3                0.01378123    9.82940898   12.62787148    -0.29071188
## mean_temp              0.05028648   12.62787148   21.97189056     0.64211293
## pct_tree_cover        -0.09908112   -0.29071188    0.64211293     5.31164400
## pct_impervious         0.65248434   -0.71842181    2.94316568     0.21810136
## mean_aadt_intensity -316.60274061  233.59559080 2237.86511575  4153.38447704
## dist_m_tri          -283.75781768  107.78779938  -92.09652567  1157.03833690
## dist_m_npl          -247.47893930  564.99435312  797.66623054  1651.13725267
## dist_m_waste_site   -256.87856646  295.90720632  595.67129800  1474.01548662
## dist_m_major_emit     75.78034383  542.77236728  731.71425416  1210.35674672
## dist_m_cafo         -796.78809693  113.64418517 1788.77467105  6740.82668034
## dist_m_mine_well    -246.15307838 -174.02154821  347.43839722  1843.07939334
## cvd_rate_adj           2.75466082   -0.19042942    3.57768901   -10.49859007
## res_rate_adj           1.92445952   -2.36449701    4.04898468     0.69481473
## violent_crime_rate     0.10159573    0.81293604    0.85366032    -0.85575848
## property_crime_rate    0.25735425    1.67359388    6.68954912    -5.59386200
## pct_less_hs            1.20446927   -0.25462044   -0.57677069    -5.96024136
## pct_unemp              0.12334849    0.18674932    0.47458851    -0.57257461
## pct_limited_eng        0.43490226   -0.35212589   -0.34012225    -2.59639577
## pct_hh_pov             0.86532874   -0.07963960    1.31570281    -1.49233483
## pct_poc                1.51246448    0.06712855   -2.21652590   -14.48950230
##                     pct_impervious mean_aadt_intensity    dist_m_tri
## mean_pm                  0.6524843           -316.6027    -283.75782
## mean_o3                 -0.7184218            233.5956     107.78780
## mean_temp                2.9431657           2237.8651     -92.09653
## pct_tree_cover           0.2181014           4153.3845    1157.03834
## pct_impervious         118.6040354          36640.1009   -7553.17944
## mean_aadt_intensity  36640.1009233       57641629.8679 1565979.88108
## dist_m_tri           -7553.1794392        1565979.8811 4608012.31878
## dist_m_npl            -729.1756706        5991441.6628 3514059.77440
## dist_m_waste_site    -5336.7915482        2680197.5003 2541111.37856
## dist_m_major_emit     5112.3800727        5142469.5768 1039857.82892
## dist_m_cafo           7343.4578780       11401543.4858 5158574.42432
## dist_m_mine_well     -1846.0608375         519042.2111 1347393.64163
## cvd_rate_adj           153.7257890          15475.7180  -40115.15023
## res_rate_adj           116.3216711          18162.7204  -24071.77748
## violent_crime_rate      14.9035752           5092.8427    -451.49611
## property_crime_rate     37.8897147          15294.9122    2942.56251
## pct_less_hs             54.1512649         -12322.2405  -14640.56309
## pct_unemp               26.7371633           4117.1570   -3067.22587
## pct_limited_eng         42.4716032          -4034.8173   -6400.69993
## pct_hh_pov              76.6828013           9296.3905   -8933.86683
## pct_poc                 82.2532162           4907.0965  -20638.86724
##                       dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm                -247.4789         -256.8786          75.78034
## mean_o3                 564.9944          295.9072         542.77237
## mean_temp               797.6662          595.6713         731.71425
## pct_tree_cover         1651.1373         1474.0155        1210.35675
## pct_impervious         -729.1757        -5336.7915        5112.38007
## mean_aadt_intensity 5991441.6628      2680197.5003     5142469.57683
## dist_m_tri          3514059.7744      2541111.3786     1039857.82892
## dist_m_npl          9755104.6822      3957347.1872     5676625.89348
## dist_m_waste_site   3957347.1872      5491944.2186      485019.21046
## dist_m_major_emit   5676625.8935       485019.2105     8317441.29166
## dist_m_cafo         7442271.8989      5706643.6152     -433351.36369
## dist_m_mine_well     373875.1037      1208648.3948    -1461468.74425
## cvd_rate_adj         -22672.7435       -49151.9480       18167.43502
## res_rate_adj          -6928.6332       -36249.6167        4967.77652
## violent_crime_rate      122.5328        -2674.5446        1187.95371
## property_crime_rate    3440.5949        -9452.8830       -5663.16784
## pct_less_hs          -15551.2855       -18040.7331        3187.36083
## pct_unemp               584.7544        -3365.1520        3672.57470
## pct_limited_eng       -3639.5214        -8519.3551        7516.33514
## pct_hh_pov            -2571.7777       -12025.9897        8216.38301
## pct_poc              -14283.4119       -17498.2028       11624.47703
##                       dist_m_cafo dist_m_mine_well   cvd_rate_adj
## mean_pm                 -796.7881        -246.1531      2.7546608
## mean_o3                  113.6442        -174.0215     -0.1904294
## mean_temp               1788.7747         347.4384      3.5776890
## pct_tree_cover          6740.8267        1843.0794    -10.4985901
## pct_impervious          7343.4579       -1846.0608    153.7257890
## mean_aadt_intensity 11401543.4858      519042.2111  15475.7180391
## dist_m_tri           5158574.4243     1347393.6416 -40115.1502286
## dist_m_npl           7442271.8989      373875.1037 -22672.7434832
## dist_m_waste_site    5706643.6152     1208648.3948 -49151.9479803
## dist_m_major_emit    -433351.3637    -1461468.7442  18167.4350205
## dist_m_cafo         33511609.3448     6740561.1503 -24023.6790132
## dist_m_mine_well     6740561.1503     3673789.1331 -29492.8084450
## cvd_rate_adj          -24023.6790      -29492.8084   1568.8304090
## res_rate_adj            7304.5199       -9245.1715   1027.7940865
## violent_crime_rate      2046.3298       -1179.9052    100.9225559
## property_crime_rate     5869.2804        -254.6397    208.2848909
## pct_less_hs           -28844.6823       -8405.9488    301.0825676
## pct_unemp              -1540.9735       -2881.3500     97.0763049
## pct_limited_eng       -10163.8795       -3977.1750    177.0027630
## pct_hh_pov             -3195.2854       -4913.3159    262.6447410
## pct_poc               -46671.0930      -22472.3318    481.1037946
##                       res_rate_adj violent_crime_rate property_crime_rate
## mean_pm                  1.9244595          0.1015957           0.2573543
## mean_o3                 -2.3644970          0.8129360           1.6735939
## mean_temp                4.0489847          0.8536603           6.6895491
## pct_tree_cover           0.6948147         -0.8557585          -5.5938620
## pct_impervious         116.3216711         14.9035752          37.8897147
## mean_aadt_intensity  18162.7203792       5092.8427356       15294.9121570
## dist_m_tri          -24071.7774777       -451.4961084        2942.5625099
## dist_m_npl           -6928.6332227        122.5327963        3440.5948584
## dist_m_waste_site   -36249.6167432      -2674.5446453       -9452.8829545
## dist_m_major_emit     4967.7765250       1187.9537119       -5663.1678442
## dist_m_cafo           7304.5198783       2046.3297823        5869.2803721
## dist_m_mine_well     -9245.1714629      -1179.9052006        -254.6397468
## cvd_rate_adj          1027.7940865        100.9225559         208.2848909
## res_rate_adj           940.1945728         76.9892329         240.8826506
## violent_crime_rate      76.9892329         25.5420603          71.9963533
## property_crime_rate    240.8826506         71.9963533         491.8000334
## pct_less_hs            185.5325753         20.6749023          22.5843969
## pct_unemp               69.2602680         10.6933742          18.5207079
## pct_limited_eng         99.1158417         11.2428807           1.1062078
## pct_hh_pov             204.6089131         27.8143880          65.8300381
## pct_poc                206.2218350         36.2845531           9.5271261
##                        pct_less_hs     pct_unemp pct_limited_eng     pct_hh_pov
## mean_pm                  1.2044693     0.1233485       0.4349023      0.8653287
## mean_o3                 -0.2546204     0.1867493      -0.3521259     -0.0796396
## mean_temp               -0.5767707     0.4745885      -0.3401222      1.3157028
## pct_tree_cover          -5.9602414    -0.5725746      -2.5963958     -1.4923348
## pct_impervious          54.1512649    26.7371633      42.4716032     76.6828013
## mean_aadt_intensity -12322.2404976  4117.1570121   -4034.8172805   9296.3904978
## dist_m_tri          -14640.5630864 -3067.2258670   -6400.6999345  -8933.8668309
## dist_m_npl          -15551.2854862   584.7543739   -3639.5214452  -2571.7776685
## dist_m_waste_site   -18040.7330880 -3365.1520125   -8519.3551489 -12025.9896947
## dist_m_major_emit     3187.3608343  3672.5746989    7516.3351376   8216.3830073
## dist_m_cafo         -28844.6823465 -1540.9735482  -10163.8795343  -3195.2853551
## dist_m_mine_well     -8405.9488274 -2881.3500245   -3977.1749583  -4913.3158874
## cvd_rate_adj           301.0825676    97.0763049     177.0027630    262.6447410
## res_rate_adj           185.5325753    69.2602680      99.1158417    204.6089131
## violent_crime_rate      20.6749023    10.6933742      11.2428807     27.8143880
## property_crime_rate     22.5843969    18.5207079       1.1062078     65.8300381
## pct_less_hs            176.2436488    36.8702016      94.5119085    114.6493750
## pct_unemp               36.8702016    25.9815492      24.8257135     39.4311861
## pct_limited_eng         94.5119085    24.8257135      82.1564459     78.3635031
## pct_hh_pov             114.6493750    39.4311861      78.3635031    139.7618779
## pct_poc                211.2594439    55.4382200     130.3042297    144.6790148
##                             pct_poc
## mean_pm                  1.51246448
## mean_o3                  0.06712855
## mean_temp               -2.21652590
## pct_tree_cover         -14.48950230
## pct_impervious          82.25321621
## mean_aadt_intensity   4907.09649773
## dist_m_tri          -20638.86723571
## dist_m_npl          -14283.41186439
## dist_m_waste_site   -17498.20282580
## dist_m_major_emit    11624.47703351
## dist_m_cafo         -46671.09304576
## dist_m_mine_well    -22472.33183580
## cvd_rate_adj           481.10379457
## res_rate_adj           206.22183502
## violent_crime_rate      36.28455311
## property_crime_rate      9.52712614
## pct_less_hs            211.25944392
## pct_unemp               55.43822005
## pct_limited_eng        130.30422969
## pct_hh_pov             144.67901481
## pct_poc                409.88652102
ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Scaling the exposure variables

X.scaled <- apply(X, 2, scale)
head(X.scaled)
##         mean_pm    mean_o3  mean_temp pct_tree_cover pct_impervious
## [1,]  1.5833180 -0.2917235 -0.1814489    -0.04443914     0.03879239
## [2,] -1.3640362  0.6205574  1.2082246     0.50870576     0.50299234
## [3,] -0.5445851  0.6498540  1.4120376    -1.19360531    -1.35153943
## [4,]  0.2607677 -0.3425882  0.5680847     2.01107115     0.27447500
## [5,] -0.5292159  0.1140521  1.0362516    -0.40884423     1.48956214
## [6,] -0.3519956  0.2770483  0.7416578    -0.39806522    -1.46928234
##      mean_aadt_intensity  dist_m_tri  dist_m_npl dist_m_waste_site
## [1,]         -0.09314684 -0.39604630 -1.67331945       -0.21569109
## [2,]         -0.01141308 -0.97887591 -0.22934656       -0.39149218
## [3,]         -1.31410486 -0.35119772 -0.80949801        0.71295064
## [4,]          0.62805092 -0.14604407 -0.89296224       -0.36283056
## [5,]         -0.78314878 -0.56928493  0.06677935       -1.33507945
## [6,]         -1.09025795  0.04202559 -0.06195205        0.01775393
##      dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,]        -0.4009504  -1.2930817       -0.6604666    0.4677498   -0.5230745
## [2,]        -1.8529984   2.4947942        2.2640219    0.5787233    1.7933345
## [3,]        -0.8037737  -1.2880039       -1.1922870   -1.5785230   -2.3093604
## [4,]        -1.3383191   1.2644356        1.4898610   -2.0799847   -1.6791619
## [5,]         0.9151010  -0.2403563        0.2814377    0.9331902    0.9665552
## [6,]        -1.0406688   0.6599675        1.1684827    0.7425635    0.8896573
##      violent_crime_rate property_crime_rate pct_less_hs   pct_unemp
## [1,]          0.1461888          -0.6678858   0.7904517  0.01287583
## [2,]         -0.9364825           0.6718153  -0.4520245 -1.28613316
## [3,]         -1.6229633          -1.3366556  -0.6306252 -1.22221641
## [4,]         -1.7021132          -0.2248212  -1.3143432 -0.28721538
## [5,]          0.3227753           0.1706146   2.4569339  3.13846569
## [6,]          0.3227753           0.1706146  -0.8419092 -0.63236396
##      pct_limited_eng  pct_hh_pov    pct_poc
## [1,]       1.6287966 -0.56661655  1.2779789
## [2,]      -0.3145189 -0.04956957 -1.6805216
## [3,]      -0.5564662 -1.40362153  0.4516629
## [4,]      -0.6872676  0.54662531 -2.0437238
## [5,]       2.9116224  2.59333462  1.3438483
## [6,]      -1.0335195 -0.80869270 -0.7845040

Variance and histograms of the exposure variables (scaled):

var(X.scaled)
##                          mean_pm      mean_o3    mean_temp pct_tree_cover
## mean_pm              1.000000000  0.006875034  0.016779077   -0.067239882
## mean_o3              0.006875034  1.000000000  0.859276109   -0.040233202
## mean_temp            0.016779077  0.859276109  1.000000000    0.059437868
## pct_tree_cover      -0.067239882 -0.040233202  0.059437868    1.000000000
## pct_impervious       0.093706751 -0.021040985  0.057654242    0.008689487
## mean_aadt_intensity -0.065222443  0.009813701  0.062882828    0.237366556
## dist_m_tri          -0.206748105  0.016015817 -0.009152774    0.233871044
## dist_m_npl          -0.123928958  0.057698489  0.054484319    0.229378511
## dist_m_waste_site   -0.171441252  0.040274372  0.054226291    0.272913179
## dist_m_major_emit    0.041097198  0.060028730  0.054126872    0.182097525
## dist_m_cafo         -0.215276049  0.006261608  0.065921075    0.505243853
## dist_m_mine_well    -0.200862414 -0.028958910  0.038671141    0.417227044
## cvd_rate_adj         0.108775391 -0.001533495  0.019269963   -0.115008119
## res_rate_adj         0.098163589 -0.024596097  0.028171083    0.009832086
## violent_crime_rate   0.031441121  0.051305593  0.036034908   -0.073469785
## property_crime_rate  0.018150458  0.024070887  0.064353009   -0.109446781
## pct_less_hs          0.141902323 -0.006117484 -0.009268570   -0.194801649
## pct_unemp            0.037848775  0.011685917  0.019863281   -0.048739950
## pct_limited_eng      0.075044931 -0.012391202 -0.008005353   -0.124289829
## pct_hh_pov           0.114482020 -0.002148676  0.023742679   -0.054771853
## pct_poc              0.116843319  0.001057576 -0.023356474   -0.310532579
##                     pct_impervious mean_aadt_intensity   dist_m_tri
## mean_pm                0.093706751        -0.065222443 -0.206748105
## mean_o3               -0.021040985         0.009813701  0.016015817
## mean_temp              0.057654242         0.062882828 -0.009152774
## pct_tree_cover         0.008689487         0.237366556  0.233871044
## pct_impervious         1.000000000         0.443137805 -0.323089805
## mean_aadt_intensity    0.443137805         1.000000000  0.096086248
## dist_m_tri            -0.323089805         0.096086248  1.000000000
## dist_m_npl            -0.021437122         0.252666254  0.524126794
## dist_m_waste_site     -0.209106459         0.150638372  0.505130772
## dist_m_major_emit      0.162771561         0.234859825  0.167966347
## dist_m_cafo            0.116480502         0.259416670  0.415121515
## dist_m_mine_well      -0.088438051         0.035667892  0.327476821
## cvd_rate_adj           0.356376451         0.051462951 -0.471806161
## res_rate_adj           0.348338943         0.078019633 -0.365714748
## violent_crime_rate     0.270777620         0.132728497 -0.041616853
## property_crime_rate    0.156883520         0.090841560  0.061812257
## pct_less_hs            0.374543388        -0.122254490 -0.513741000
## pct_unemp              0.481651675         0.106389013 -0.280321508
## pct_limited_eng        0.430257154        -0.058632029 -0.328965104
## pct_hh_pov             0.595598881         0.103574267 -0.352036987
## pct_poc                0.373053688         0.031924540 -0.474894591
##                       dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm             -0.123928958       -0.17144125        0.04109720
## mean_o3              0.057698489        0.04027437        0.06002873
## mean_temp            0.054484319        0.05422629        0.05412687
## pct_tree_cover       0.229378511        0.27291318        0.18209753
## pct_impervious      -0.021437122       -0.20910646        0.16277156
## mean_aadt_intensity  0.252666254        0.15063837        0.23485982
## dist_m_tri           0.524126794        0.50513077        0.16796635
## dist_m_npl           1.000000000        0.54066111        0.63020150
## dist_m_waste_site    0.540661105        1.00000000        0.07176307
## dist_m_major_emit    0.630201503        0.07176307        1.00000000
## dist_m_cafo          0.411615692        0.42064918       -0.02595659
## dist_m_mine_well     0.062453023        0.26907900       -0.26438545
## cvd_rate_adj        -0.183273683       -0.52952891        0.15904160
## res_rate_adj        -0.072347368       -0.50446552        0.05617697
## violent_crime_rate   0.007762622       -0.22581814        0.08150358
## property_crime_rate  0.049673332       -0.18188921       -0.08854627
## pct_less_hs         -0.375053817       -0.57987500        0.08324911
## pct_unemp            0.036730344       -0.28171444        0.24982923
## pct_limited_eng     -0.128560483       -0.40107246        0.28753482
## pct_hh_pov          -0.069650316       -0.43407363        0.24098579
## pct_poc             -0.225883326       -0.36880650        0.19908876
##                      dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm             -0.215276049     -0.200862414  0.108775391  0.098163589
## mean_o3              0.006261608     -0.028958910 -0.001533495 -0.024596097
## mean_temp            0.065921075      0.038671141  0.019269963  0.028171083
## pct_tree_cover       0.505243853      0.417227044 -0.115008119  0.009832086
## pct_impervious       0.116480502     -0.088438051  0.356376451  0.348338943
## mean_aadt_intensity  0.259416670      0.035667892  0.051462951  0.078019633
## dist_m_tri           0.415121515      0.327476821 -0.471806161 -0.365714748
## dist_m_npl           0.411615692      0.062453023 -0.183273683 -0.072347368
## dist_m_waste_site    0.420649183      0.269079002 -0.529528911 -0.504465523
## dist_m_major_emit   -0.025956591     -0.264385448  0.159041603  0.056176970
## dist_m_cafo          1.000000000      0.607493028 -0.104774085  0.041151452
## dist_m_mine_well     0.607493028      1.000000000 -0.388482105 -0.157307340
## cvd_rate_adj        -0.104774085     -0.388482105  1.000000000  0.846270584
## res_rate_adj         0.041151452     -0.157307340  0.846270584  1.000000000
## violent_crime_rate   0.069943928     -0.121804137  0.504164518  0.496813238
## property_crime_rate  0.045718601     -0.005990662  0.237123988  0.354243895
## pct_less_hs         -0.375328359     -0.330348920  0.572586196  0.455779267
## pct_unemp           -0.052223385     -0.294921467  0.480831284  0.443141860
## pct_limited_eng     -0.193705095     -0.228926866  0.493027592  0.356626311
## pct_hh_pov          -0.046689330     -0.216831917  0.560901170  0.564444590
## pct_poc             -0.398215822     -0.579107525  0.599955397  0.332195663
##                     violent_crime_rate property_crime_rate  pct_less_hs
## mean_pm                    0.031441121         0.018150458  0.141902323
## mean_o3                    0.051305593         0.024070887 -0.006117484
## mean_temp                  0.036034908         0.064353009 -0.009268570
## pct_tree_cover            -0.073469785        -0.109446781 -0.194801649
## pct_impervious             0.270777620         0.156883520  0.374543388
## mean_aadt_intensity        0.132728497         0.090841560 -0.122254490
## dist_m_tri                -0.041616853         0.061812257 -0.513741000
## dist_m_npl                 0.007762622         0.049673332 -0.375053817
## dist_m_waste_site         -0.225818142        -0.181889213 -0.579874999
## dist_m_major_emit          0.081503580        -0.088546273  0.083249114
## dist_m_cafo                0.069943928         0.045718601 -0.375328359
## dist_m_mine_well          -0.121804137        -0.005990662 -0.330348920
## cvd_rate_adj               0.504164518         0.237123988  0.572586196
## res_rate_adj               0.496813238         0.354243895  0.455779267
## violent_crime_rate         1.000000000         0.642374450  0.308147582
## property_crime_rate        0.642374450         1.000000000  0.076710972
## pct_less_hs                0.308147582         0.076710972  1.000000000
## pct_unemp                  0.415101478         0.163844091  0.544861664
## pct_limited_eng            0.245430660         0.005503280  0.785432692
## pct_hh_pov                 0.465529473         0.251093497  0.730500622
## pct_poc                    0.354618997         0.021219533  0.786009104
##                       pct_unemp pct_limited_eng   pct_hh_pov      pct_poc
## mean_pm              0.03784877     0.075044931  0.114482020  0.116843319
## mean_o3              0.01168592    -0.012391202 -0.002148676  0.001057576
## mean_temp            0.01986328    -0.008005353  0.023742679 -0.023356474
## pct_tree_cover      -0.04873995    -0.124289829 -0.054771853 -0.310532579
## pct_impervious       0.48165167     0.430257154  0.595598881  0.373053688
## mean_aadt_intensity  0.10638901    -0.058632029  0.103574267  0.031924540
## dist_m_tri          -0.28032151    -0.328965104 -0.352036987 -0.474894591
## dist_m_npl           0.03673034    -0.128560483 -0.069650316 -0.225883326
## dist_m_waste_site   -0.28171444    -0.401072461 -0.434073632 -0.368806502
## dist_m_major_emit    0.24982923     0.287534819  0.240985793  0.199088756
## dist_m_cafo         -0.05222339    -0.193705095 -0.046689330 -0.398215822
## dist_m_mine_well    -0.29492147    -0.228926866 -0.216831917 -0.579107525
## cvd_rate_adj         0.48083128     0.493027592  0.560901170  0.599955397
## res_rate_adj         0.44314186     0.356626311  0.564444590  0.332195663
## violent_crime_rate   0.41510148     0.245430660  0.465529473  0.354618997
## property_crime_rate  0.16384409     0.005503280  0.251093497  0.021219533
## pct_less_hs          0.54486166     0.785432692  0.730500622  0.786009104
## pct_unemp            1.00000000     0.537339041  0.654354292  0.537211051
## pct_limited_eng      0.53733904     1.000000000  0.731305192  0.710077699
## pct_hh_pov           0.65435429     0.731305192  1.000000000  0.604476415
## pct_poc              0.53721105     0.710077699  0.604476415  1.000000000
ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.2 Covariate data

Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.

W <- select(hs_data2, 
            lat, lon, lat_lon_int,
            ed_no_hs, ed_hs, ed_aa, ed_4yr,
            low_bmi, ovwt_bmi, obese_bmi,
            concep_spring, concep_summer, concep_fall,
            concep_2010, concep_2011, concep_2012, concep_2013,
            maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
            male, gest_age_w) %>%
  as.matrix()
head(W)
##           lat       lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,] 39.79402 -104.8133   -4170.944        0     0     1      0       0
## [2,] 39.62671 -104.9927   -4160.517        0     0     1      0       0
## [3,] 39.79134 -104.7669   -4168.814        0     0     0      1       0
## [4,] 39.68050 -104.9451   -4164.274        0     0     1      0       0
## [5,] 39.74073 -104.8516   -4166.881        1     0     0      0       0
## [6,] 39.69147 -104.7602   -4158.086        0     1     0      0       0
##      ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,]        0         0             0             0           0           0
## [2,]        0         0             0             0           0           1
## [3,]        0         0             1             0           0           1
## [4,]        0         0             0             0           0           1
## [5,]        1         0             1             0           0           1
## [6,]        0         1             0             0           0           1
##      concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,]           0           0           0           19          0       1
## [2,]           0           0           0           36          0       0
## [3,]           0           0           0           30          0       0
## [4,]           0           0           0           22          0       0
## [5,]           0           0           0           32          0       1
## [6,]           0           0           0           27          0       0
##      mean_cpss mean_epsd male gest_age_w
## [1,]        29         0    0   40.57143
## [2,]        19         2    1   35.85714
## [3,]        15         0    1   38.42857
## [4,]        17         1    0   40.71429
## [5,]        18         0    0   40.28571
## [6,]        17         7    0   40.00000

Scaled the non-binary (continuous) covariates

colnames(W)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"          "gest_age_w"
W.s <- apply(W[,c(1, 2, 3, 18, 21, 22, 24)], 2, scale) #' just the continuous ones

W.scaled <- cbind(W.s[,1:3],
                  W[,4:17], W.s[,4],
                  W[,19:20], W.s[,5:6],
                  W[,23], W.s[,7])
colnames(W.scaled)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   ""              "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     ""              ""
colnames(W.scaled) <- colnames(W)
head(W.scaled)
##             lat         lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,]  1.1167843  0.51514286  -0.7374184        0     0     1      0       0
## [2,] -1.8516422 -2.09256135   0.7445400        0     0     1      0       0
## [3,]  1.0692021  1.19072454  -0.4346320        0     0     0      1       0
## [4,] -0.8972660 -1.40025129   0.2104678        0     0     1      0       0
## [5,]  0.1713509 -0.04176901  -0.1600238        1     0     0      0       0
## [6,] -0.7026663  1.28759109   1.0899619        0     1     0      0       0
##      ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,]        0         0             0             0           0           0
## [2,]        0         0             0             0           0           1
## [3,]        0         0             1             0           0           1
## [4,]        0         0             0             0           0           1
## [5,]        1         0             1             0           0           1
## [6,]        0         1             0             0           0           1
##      concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,]           0           0           0   -0.9872932          0       1
## [2,]           0           0           0    1.7854996          0       0
## [3,]           0           0           0    0.8068668          0       0
## [4,]           0           0           0   -0.4979769          0       0
## [5,]           0           0           0    1.1330778          0       1
## [6,]           0           0           0    0.3175505          0       0
##        mean_cpss  mean_epsd male gest_age_w
## [1,]  2.95983287 -1.3146057    0  0.7383142
## [2,]  0.17922225 -0.7742175    1 -1.5631894
## [3,] -0.93302200 -1.3146057    1 -0.3078238
## [4,] -0.37689988 -1.0444116    0  0.8080568
## [5,] -0.09883881 -1.3146057    0  0.5988292
## [6,] -0.37689988  0.5767527    0  0.4593441
summary(W.scaled)
##       lat                 lon           lat_lon_int          ed_no_hs   
##  Min.   :-2.713877   Min.   :-2.9703   Min.   :-3.84454   Min.   :0.00  
##  1st Qu.:-0.641686   1st Qu.:-0.3049   1st Qu.:-0.39665   1st Qu.:0.00  
##  Median :-0.004541   Median : 0.1978   Median : 0.03426   Median :0.00  
##  Mean   : 0.000000   Mean   : 0.0000   Mean   : 0.00000   Mean   :0.25  
##  3rd Qu.: 0.513104   3rd Qu.: 0.5538   3rd Qu.: 0.61126   3rd Qu.:0.25  
##  Max.   : 4.719081   Max.   : 2.1774   Max.   : 2.93499   Max.   :1.00  
##      ed_hs            ed_aa            ed_4yr          low_bmi      
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.2854   Mean   :0.3009   Mean   :0.1084   Mean   :0.0354  
##  3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:0.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##     ovwt_bmi       obese_bmi      concep_spring  concep_summer  
##  Min.   :0.000   Min.   :0.0000   Min.   :0.00   Min.   :0.000  
##  1st Qu.:0.000   1st Qu.:0.0000   1st Qu.:0.00   1st Qu.:0.000  
##  Median :0.000   Median :0.0000   Median :0.00   Median :0.000  
##  Mean   :0.292   Mean   :0.2588   Mean   :0.25   Mean   :0.219  
##  3rd Qu.:1.000   3rd Qu.:1.0000   3rd Qu.:0.25   3rd Qu.:0.000  
##  Max.   :1.000   Max.   :1.0000   Max.   :1.00   Max.   :1.000  
##   concep_fall      concep_2010      concep_2011      concep_2012    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.2832   Mean   :0.1659   Mean   :0.3164   Mean   :0.2898  
##  3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##   concep_2013      maternal_age       any_smoker       smokeSH      
##  Min.   :0.0000   Min.   :-1.4766   Min.   :0.000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:-0.8242   1st Qu.:0.000   1st Qu.:0.0000  
##  Median :0.0000   Median :-0.1718   Median :0.000   Median :0.0000  
##  Mean   :0.2257   Mean   : 0.0000   Mean   :0.104   Mean   :0.3319  
##  3rd Qu.:0.0000   3rd Qu.: 0.8069   3rd Qu.:0.000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   : 2.9272   Max.   :1.000   Max.   :1.0000  
##    mean_cpss          mean_epsd            male          gest_age_w     
##  Min.   :-5.10394   Min.   :-1.3146   Min.   :0.0000   Min.   :-6.6544  
##  1st Qu.:-0.52752   1st Qu.:-0.7742   1st Qu.:0.0000   1st Qu.:-0.3078  
##  Median : 0.01702   Median :-0.1438   Median :1.0000   Median : 0.1804  
##  Mean   : 0.00000   Mean   : 0.0000   Mean   :0.5111   Mean   : 0.0000  
##  3rd Qu.: 0.54997   3rd Qu.: 0.5768   3rd Qu.:1.0000   3rd Qu.: 0.5988  
##  Max.   : 4.07208   Max.   : 5.3051   Max.   :1.0000   Max.   : 2.6911

Variance and histograms for the scaled covariates

var(W.scaled)
##                         lat           lon  lat_lon_int     ed_no_hs
## lat            1.0000000000 -0.2197126628 -0.925354901  0.023704345
## lon           -0.2197126628  1.0000000000  0.573149965 -0.020706192
## lat_lon_int   -0.9253549015  0.5731499653  1.000000000 -0.027956367
## ed_no_hs       0.0237043446 -0.0207061919 -0.027956367  0.187915743
## ed_hs         -0.0118544823  0.0341795076  0.023258551 -0.071507761
## ed_aa          0.0074435062 -0.0103199888 -0.010249527 -0.075388027
## ed_4yr        -0.0110564389  0.0208198361  0.017353352 -0.027161863
## low_bmi       -0.0001880928 -0.0056988431 -0.002050855 -0.006651885
## ovwt_bmi       0.0248936444  0.0136211023 -0.015634135  0.011086475
## obese_bmi      0.0107122204 -0.0280748233 -0.019899866 -0.004988914
## concep_spring -0.0223303960  0.0011338637  0.019209169 -0.007206208
## concep_summer  0.0203779870 -0.0366082745 -0.031356869  0.002771619
## concep_fall    0.0058156155  0.0376700058  0.009742659  0.019955654
## concep_2010    0.0219575397  0.0233177984 -0.009385304 -0.006097561
## concep_2011    0.0063177657 -0.0094195638 -0.008977235  0.018292683
## concep_2012    0.0156618197  0.0002195065 -0.013078318 -0.008314856
## concep_2013   -0.0464133651 -0.0152599647  0.033075931 -0.003325942
## maternal_age  -0.0302790950 -0.0162109126  0.019088658 -0.119345460
## any_smoker    -0.0054630028  0.0080912190  0.007738581  0.009423503
## smokeSH        0.0283665743  0.0097078774 -0.020047891  0.012195122
## mean_cpss     -0.0247080882  0.0477415558  0.039275067 -0.067717014
## mean_epsd     -0.0326272603  0.0794941258  0.058301007  0.050748754
## male           0.0320040663 -0.0174533275 -0.033655475 -0.023835920
## gest_age_w     0.0428155858 -0.0443601833 -0.053216199  0.011327363
##                       ed_hs         ed_aa        ed_4yr       low_bmi
## lat           -0.0118544823  0.0074435062 -0.0110564389 -0.0001880928
## lon            0.0341795076 -0.0103199888  0.0208198361 -0.0056988431
## lat_lon_int    0.0232585506 -0.0102495267  0.0173533517 -0.0020508553
## ed_no_hs      -0.0715077605 -0.0753880266 -0.0271618625 -0.0066518847
## ed_hs          0.2043982890 -0.0860624375 -0.0310077900 -0.0056904028
## ed_aa         -0.0860624375  0.2108196142 -0.0326903832  0.0137158331
## ed_4yr        -0.0310077900 -0.0326903832  0.0968692973 -0.0016286325
## low_bmi       -0.0056904028  0.0137158331 -0.0016286325  0.0342209054
## ovwt_bmi      -0.0125777525  0.0050624963  0.0037478170 -0.0103604576
## obese_bmi      0.0168700822  0.0017659871  0.0007014893 -0.0091831329
## concep_spring  0.0083148559  0.0110864745 -0.0116407982 -0.0022172949
## concep_summer -0.0005641348 -0.0106155446  0.0028108628  0.0055334262
## concep_fall   -0.0033946196 -0.0166591449  0.0047092989 -0.0033946196
## concep_2010   -0.0008977101  0.0009614819  0.0085797539  0.0007652611
## concep_2011   -0.0106695053  0.0021584287 -0.0055481428  0.0065145301
## concep_2012    0.0124453035 -0.0031395326 -0.0048809921 -0.0036300846
## concep_2013   -0.0002452760 -0.0015305221  0.0020897514 -0.0035712183
## maternal_age  -0.0708295621  0.0194492453  0.1014068354 -0.0173049316
## any_smoker    -0.0097865118  0.0174244059 -0.0112974118  0.0051802288
## smokeSH        0.0092910543  0.0174440280 -0.0271863901  0.0037478170
## mean_cpss     -0.0170704310  0.0482904416  0.0212189132  0.0092354197
## mean_epsd     -0.0009814900  0.0001820274 -0.0280010721  0.0143704449
## male           0.0023791771  0.0166199007  0.0065586798 -0.0048270314
## gest_age_w     0.0064377356 -0.0428762705  0.0228446044 -0.0133948146
##                   ovwt_bmi     obese_bmi concep_spring concep_summer
## lat            0.024893644  0.0107122204  -0.022330396  0.0203779870
## lon            0.013621102 -0.0280748233   0.001133864 -0.0366082745
## lat_lon_int   -0.015634135 -0.0198998660   0.019209169 -0.0313568686
## ed_no_hs       0.011086475 -0.0049889135  -0.007206208  0.0027716186
## ed_hs         -0.012577752  0.0168700822   0.008314856 -0.0005641348
## ed_aa          0.005062496  0.0017659871   0.011086475 -0.0106155446
## ed_4yr         0.003747817  0.0007014893  -0.011640798  0.0028108628
## low_bmi       -0.010360458 -0.0091831329  -0.002217295  0.0055334262
## ovwt_bmi       0.207209152 -0.0757608461   0.004434590 -0.0131075486
## obese_bmi     -0.075760846  0.1922718443  -0.018292683 -0.0058228519
## concep_spring  0.004434590 -0.0182926829   0.187915743 -0.0548780488
## concep_summer -0.013107549 -0.0058228519  -0.054878049  0.1714331966
## concep_fall    0.005808135  0.0085748484  -0.070953437 -0.0621627455
## concep_2010   -0.008653337 -0.0009173322  -0.023835920  0.0101397092
## concep_2011    0.013833566 -0.0111208131   0.007206208 -0.0095804800
## concep_2012   -0.002786335  0.0157221906  -0.010532151 -0.0126219022
## concep_2013   -0.001746365 -0.0031100995   0.027716186  0.0125483194
## maternal_age   0.013377957  0.0577876541  -0.020975869  0.0017154510
## any_smoker    -0.006043600 -0.0048025038   0.002771619  0.0037821557
## smokeSH       -0.019523968 -0.0040519593   0.003325942 -0.0085454153
## mean_cpss     -0.020707855 -0.0033427927   0.019318359  0.0132411329
## mean_epsd     -0.020709593  0.0110314349   0.005616562 -0.0174792697
## male           0.005631537  0.0026735082  -0.019401330 -0.0124060593
## gest_age_w     0.024184017 -0.0142894672  -0.017280994  0.0199550304
##                 concep_fall   concep_2010  concep_2011   concep_2012
## lat            0.0058156155  0.0219575397  0.006317766  0.0156618197
## lon            0.0376700058  0.0233177984 -0.009419564  0.0002195065
## lat_lon_int    0.0097426586 -0.0093853043 -0.008977235 -0.0130783182
## ed_no_hs       0.0199556541 -0.0060975610  0.018292683 -0.0083148559
## ed_hs         -0.0033946196 -0.0008977101 -0.010669505  0.0124453035
## ed_aa         -0.0166591449  0.0009614819  0.002158429 -0.0031395326
## ed_4yr         0.0047092989  0.0085797539 -0.005548143 -0.0048809921
## low_bmi       -0.0033946196  0.0007652611  0.006514530 -0.0036300846
## ovwt_bmi       0.0058081353 -0.0086533367  0.013833566 -0.0027863352
## obese_bmi      0.0085748484 -0.0009173322 -0.011120813  0.0157221906
## concep_spring -0.0709534368 -0.0238359202  0.007206208 -0.0105321508
## concep_summer -0.0621627455  0.0101397092 -0.009580480 -0.0126219022
## concep_fall    0.2034417126  0.0216431529 -0.012185311  0.0108706316
## concep_2010    0.0216431529  0.1387035693 -0.052611699 -0.0481967310
## concep_2011   -0.0121853109 -0.0526116987  0.216760199 -0.0918951004
## concep_2012    0.0108706316 -0.0481967310 -0.091895100  0.2062820085
## concep_2013   -0.0197005671 -0.0375272256 -0.071551910 -0.0655475541
## maternal_age  -0.0125842410 -0.0133747567 -0.049399227  0.0459459217
## any_smoker    -0.0006867728 -0.0017708926  0.020245080 -0.0124649255
## smokeSH       -0.0054941821  0.0024625709  0.018945117 -0.0232227302
## mean_cpss      0.0093518172  0.0092526974 -0.021988228 -0.0088771334
## mean_epsd      0.0496616702 -0.0299985136  0.031899640 -0.0137008756
## male           0.0123815317  0.0103555521  0.002035791  0.0089820066
## gest_age_w     0.0068109922  0.0120574543 -0.029097251 -0.0198243392
##                 concep_2013 maternal_age    any_smoker       smokeSH
## lat           -0.0464133651 -0.030279095 -0.0054630028  0.0283665743
## lon           -0.0152599647 -0.016210913  0.0080912190  0.0097078774
## lat_lon_int    0.0330759314  0.019088658  0.0077385809 -0.0200478908
## ed_no_hs      -0.0033259424 -0.119345460  0.0094235033  0.0121951220
## ed_hs         -0.0002452760 -0.070829562 -0.0097865118  0.0092910543
## ed_aa         -0.0015305221  0.019449245  0.0174244059  0.0174440280
## ed_4yr         0.0020897514  0.101406835 -0.0112974118 -0.0271863901
## low_bmi       -0.0035712183 -0.017304932  0.0051802288  0.0037478170
## ovwt_bmi      -0.0017463650  0.013377957 -0.0060436003 -0.0195239684
## obese_bmi     -0.0031100995  0.057787654 -0.0048025038 -0.0040519593
## concep_spring  0.0277161863 -0.020975869  0.0027716186  0.0033259424
## concep_summer  0.0125483194  0.001715451  0.0037821557 -0.0085454153
## concep_fall   -0.0197005671 -0.012584241 -0.0006867728 -0.0054941821
## concep_2010   -0.0375272256 -0.013374757 -0.0017708926  0.0024625709
## concep_2011   -0.0715519102 -0.049399227  0.0202450798  0.0189451170
## concep_2012   -0.0655475541  0.045945922 -0.0124649255 -0.0232227302
## concep_2013    0.1751270530  0.019017182 -0.0057787022  0.0003335753
## maternal_age   0.0190171821  1.000000000 -0.0265798885 -0.1236724928
## any_smoker    -0.0057787022 -0.026579889  0.0933765673  0.0496732924
## smokeSH        0.0003335753 -0.123672493  0.0496732924  0.2222200420
## mean_cpss      0.0150498420  0.047512237  0.0270005987  0.0695757378
## mean_epsd      0.0147146181 -0.090511822  0.0336448052  0.0944708964
## male          -0.0202401742  0.058130104 -0.0066960344 -0.0014618449
## gest_age_w     0.0352270759  0.048984057 -0.0152234640 -0.0504214595
##                  mean_cpss     mean_epsd         male   gest_age_w
## lat           -0.024708088 -0.0326272603  0.032004066  0.042815586
## lon            0.047741556  0.0794941258 -0.017453327 -0.044360183
## lat_lon_int    0.039275067  0.0583010075 -0.033655475 -0.053216199
## ed_no_hs      -0.067717014  0.0507487538 -0.023835920  0.011327363
## ed_hs         -0.017070431 -0.0009814900  0.002379177  0.006437736
## ed_aa          0.048290442  0.0001820274  0.016619901 -0.042876270
## ed_4yr         0.021218913 -0.0280010721  0.006558680  0.022844604
## low_bmi        0.009235420  0.0143704449 -0.004827031 -0.013394815
## ovwt_bmi      -0.020707855 -0.0207095934  0.005631537  0.024184017
## obese_bmi     -0.003342793  0.0110314349  0.002673508 -0.014289467
## concep_spring  0.019318359  0.0056165615 -0.019401330 -0.017280994
## concep_summer  0.013241133 -0.0174792697 -0.012406059  0.019955030
## concep_fall    0.009351817  0.0496616702  0.012381532  0.006810992
## concep_2010    0.009252697 -0.0299985136  0.010355552  0.012057454
## concep_2011   -0.021988228  0.0318996396  0.002035791 -0.029097251
## concep_2012   -0.008877133 -0.0137008756  0.008982007 -0.019824339
## concep_2013    0.015049842  0.0147146181 -0.020240174  0.035227076
## maternal_age   0.047512237 -0.0905118217  0.058130104  0.048984057
## any_smoker     0.027000599  0.0336448052 -0.006696034 -0.015223464
## smokeSH        0.069575738  0.0944708964 -0.001461845 -0.050421459
## mean_cpss      1.000000000  0.4555278461 -0.014248699 -0.058556609
## mean_epsd      0.455527846  1.0000000000  0.007542429 -0.136977722
## male          -0.014248699  0.0075424291  0.250431686  0.005788385
## gest_age_w    -0.058556609 -0.1369777217  0.005788385  1.000000000
ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.3 Response data: birth weight (in grams)

Y <- select(hs_data2, birth_weight) %>%
  as.matrix()
head(Y)
##      birth_weight
## [1,]         2860
## [2,]         2755
## [3,]         3355
## [4,]         3810
## [5,]         2930
## [6,]         3235

Distribution of birth weight and scaled birth weight

hist(Y, breaks = 20)

hist(scale(Y), breaks = 20)

Dropping gest_age_w from the covariates

colnames(W.scaled)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"          "gest_age_w"
W.scaled2 <- W.scaled[,-c(ncol(W.scaled))]
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"

2 RIDGE regression

To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.

set.seed(123)

library(glmnet)
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack
## Loaded glmnet 4.0-2
lambda_seq <- 10^seq(4, -4, by = -.05)

#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
                      standardize = T, standardize.response = T)
plot(ridge_cv)

best_lambda <- ridge_cv$lambda.min
best_lambda
## [1] 10000
#' Fit the model using the best_lambda
bw_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
                   standardize = T, standardize.response = T)
summary(bw_ridge)
##           Length Class     Mode   
## a0         1     -none-    numeric
## beta      21     dgCMatrix S4     
## df         1     -none-    numeric
## dim        2     -none-    numeric
## lambda     1     -none-    numeric
## dev.ratio  1     -none-    numeric
## nulldev    1     -none-    numeric
## npasses    1     -none-    numeric
## jerr       1     -none-    numeric
## offset     1     -none-    logical
## call       7     -none-    call   
## nobs       1     -none-    numeric

Ridge regression coefficients

coef(bw_ridge)
## 22 x 1 sparse Matrix of class "dgCMatrix"
##                                   s0
## (Intercept)         3209.79864217149
## mean_pm               -1.17201110995
## mean_o3               -0.96060373712
## mean_temp             -0.57183600596
## pct_tree_cover         0.17202004715
## pct_impervious         0.01490879710
## mean_aadt_intensity    0.00010063296
## dist_m_tri             0.00012909382
## dist_m_npl             0.00014590679
## dist_m_waste_site      0.00031053298
## dist_m_major_emit      0.00036515555
## dist_m_cafo           -0.00008288071
## dist_m_mine_well      -0.00026813254
## cvd_rate_adj          -0.03527224850
## res_rate_adj          -0.03252749603
## violent_crime_rate    -0.07375766433
## property_crime_rate    0.00637844214
## pct_less_hs            0.00093472723
## pct_unemp             -0.41845995412
## pct_limited_eng       -0.02741255114
## pct_hh_pov             0.00939489388
## pct_poc               -0.04579457829

Ridge regression predictions

ridge_pred <- predict(bw_ridge, newx = X)
plot(Y, ridge_pred)

actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))

The R2 value for this model is 0. Based on these results, it doesn’t look like there’s much here.

3 Nonparametric Bayesian Shrinkage (NPB): Birth weight

3.1 Finding the NPB priors

3.1.1 Vignette Priors

set.seed(123)

priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1)

fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]    -0.05695777  2.936959      0.00000      0.00000 0.012
##  [2,]    -2.24207523 14.551354    -35.68220      0.00000 0.040
##  [3,]    -0.60321006  6.334358      0.00000      0.00000 0.016
##  [4,]     0.24631849  4.108479      0.00000      0.00000 0.008
##  [5,]    -0.01202969  1.647202      0.00000      0.00000 0.010
##  [6,]     0.06117692  1.075446      0.00000      0.00000 0.004
##  [7,]     0.40028362  3.413717      0.00000      0.00000 0.020
##  [8,]     0.50624633  4.722717      0.00000      0.00000 0.014
##  [9,]     1.31016373  9.364072      0.00000     18.84844 0.032
## [10,]     0.22695955  2.513061      0.00000      0.00000 0.014
## [11,]    -1.69432196 20.001543      0.00000      0.00000 0.028
## [12,]    -0.25492222  3.585282      0.00000      0.00000 0.012
## [13,]    -0.73466078  6.461440      0.00000      0.00000 0.022
## [14,]    -1.83830178 10.559279    -43.33420      0.00000 0.038
## [15,]     0.03930663  6.537587      0.00000      0.00000 0.022
## [16,]     0.18015253  2.319517      0.00000      0.00000 0.014
## [17,]     0.03130824  1.361797      0.00000      0.00000 0.012
## [18,]    -1.87807674 10.840157    -40.52837      0.00000 0.036
## [19,]    -0.15310310  3.071736      0.00000      0.00000 0.014
## [20,]     0.08208676  1.379057      0.00000      0.00000 0.006
## [21,]     0.17156932  3.733147      0.00000      0.00000 0.012
plot(fit.npb.1$beta[,1], type = "l")

plot(fit.npb.1$beta[,2], type = "l")

plot(fit.npb.1$beta[,13], type = "l")

3.1.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10

priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 10, sig2inv.mu1 = 10)

fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]     -1.2529045 10.730147   -31.330506    18.380557 0.258
##  [2,]    -13.0881671 28.085738   -93.068549    12.242981 0.394
##  [3,]     -4.9825663 18.016028   -55.476330    20.865449 0.352
##  [4,]      0.9588258 10.849730   -22.423150    30.141911 0.270
##  [5,]     -2.9542788 14.416081   -51.271414    17.225799 0.290
##  [6,]      3.0709359 12.660109   -14.441693    37.265962 0.292
##  [7,]      2.7376292 13.300219   -22.675584    38.331700 0.284
##  [8,]      2.2880182 13.522575   -20.563550    35.574735 0.290
##  [9,]      7.0934095 21.575502   -18.610142    73.395204 0.350
## [10,]      8.2643408 19.434287    -5.064555    69.564690 0.324
## [11,]     -6.8637718 29.581977   -88.218785    30.909406 0.370
## [12,]     -6.7185881 18.674257   -61.136654    16.151969 0.370
## [13,]     -7.0997808 19.273637   -66.539792    15.104492 0.336
## [14,]    -13.2076165 25.579187   -89.779409     7.673275 0.420
## [15,]      6.9815853 18.030428    -6.311038    64.075998 0.306
## [16,]      3.0213070 12.731469   -14.934310    45.493061 0.250
## [17,]      0.8139605 13.690379   -25.523666    32.665027 0.300
## [18,]    -17.6271428 28.414522   -94.024979     2.988976 0.482
## [19,]     -1.3052406  9.930916   -30.761027    16.085328 0.246
## [20,]      1.0247298 11.138782   -20.880505    28.447281 0.264
## [21,]      0.2244173 12.085502   -26.647282    26.043596 0.244
plot(fit.npb.24$beta[,1], type = "l")

plot(fit.npb.24$beta[,2], type = "l")

plot(fit.npb.24$beta[,13], type = "l")

3.2 Run the NPB model with temperaure and ozone

Below I’ve used the set of priors labeled “24” and set scaleY = T

The priors are as follows: r priors.npb.24

Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.

priors.npb <- priors.npb.24

#' Exposures 
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"
# fit.npb2 <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
#                scaleY = TRUE,
#                priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb2, file = here::here("Results", "NPB_Birth_Weight_v4c.2.rdata"))

load(here::here("Results", "NPB_Birth_Weight_v4c.2.rdata"))
npb.sum2 <- summary(fit.npb2)

3.2.1 First, main effect regression coefficients with PIPs

rownames(npb.sum2$main.effects) <- colnames(X.scaled)
npb.sum2$main.effects
##                     Posterior Mean       SD 95% CI Lower 95% CI Upper    PIP
## mean_pm                -15.0400987 28.63075   -94.306370    13.071278 0.4520
## mean_o3                -15.4764202 31.29159  -103.482537    11.847902 0.4292
## mean_temp                0.8637020 17.33207   -36.221436    43.815375 0.3156
## pct_tree_cover           1.1703175 10.61831   -19.920745    31.349966 0.2704
## pct_impervious          -0.9943910 10.01024   -29.385274    19.572781 0.2476
## mean_aadt_intensity      3.3078308 11.53627   -10.500466    38.221276 0.2780
## dist_m_tri               3.5042320 13.59236   -15.322403    43.897194 0.2984
## dist_m_npl               0.8927001 15.46597   -28.775335    31.998629 0.2868
## dist_m_waste_site        8.4303467 19.94186    -9.894573    65.388107 0.3760
## dist_m_major_emit        7.7876799 18.99636    -8.721286    63.218522 0.3488
## dist_m_cafo             -5.3754130 30.34930   -83.783903    36.032849 0.3592
## dist_m_mine_well        -0.3763322 13.37283   -33.871019    28.713684 0.2888
## cvd_rate_adj            -2.4834185 15.79817   -47.777595    27.253051 0.3160
## res_rate_adj           -16.3563994 28.97361   -93.578118     6.286628 0.4468
## violent_crime_rate       4.4861756 14.57330   -10.361279    48.603636 0.2984
## property_crime_rate      1.8534708 10.95868   -15.054892    31.426820 0.2596
## pct_less_hs              1.4767809 13.55808   -22.218749    36.400179 0.2752
## pct_unemp              -12.2979023 23.95060   -80.167506     7.271875 0.4056
## pct_limited_eng         -2.2029122 12.87752   -39.750439    19.373807 0.2668
## pct_hh_pov               1.3132853 12.23588   -21.524834    34.543378 0.2632
## pct_poc                  1.6494979 12.60715   -19.403174    35.466016 0.2824

3.2.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum2$interactions
##         Posterior Mean          SD 95% CI Lower 95% CI Upper    PIP
##   [1,]   28.1887482288 49.05514274     0.000000     148.2339 0.2744
##   [2,]    1.3131081276 10.35393346     0.000000       0.0000 0.0232
##   [3,]   -0.0917138713  1.53858175     0.000000       0.0000 0.0060
##   [4,]   -0.0131010052  0.88838275     0.000000       0.0000 0.0040
##   [5,]    0.0736029976  2.15373437     0.000000       0.0000 0.0068
##   [6,]   -0.0448202473  0.94827597     0.000000       0.0000 0.0040
##   [7,]   -0.0285005244  1.38220859     0.000000       0.0000 0.0064
##   [8,]   -0.1261093762  1.79679962     0.000000       0.0000 0.0076
##   [9,]   -0.1319406190  2.04625050     0.000000       0.0000 0.0072
##  [10,]   -0.0445847595  0.86241997     0.000000       0.0000 0.0032
##  [11,]   -0.0530454799  1.27574895     0.000000       0.0000 0.0056
##  [12,]   -0.0441589444  1.05319037     0.000000       0.0000 0.0044
##  [13,]   -0.0058957564  0.88336896     0.000000       0.0000 0.0036
##  [14,]    0.0115685346  0.99151068     0.000000       0.0000 0.0032
##  [15,]    0.0982782784  2.45416369     0.000000       0.0000 0.0044
##  [16,]   -0.0681654966  1.24884636     0.000000       0.0000 0.0040
##  [17,]   -0.0139580496  0.80125927     0.000000       0.0000 0.0028
##  [18,]   -0.1964555561  2.56385226     0.000000       0.0000 0.0084
##  [19,]   -0.0481477094  0.96573055     0.000000       0.0000 0.0052
##  [20,]   -0.0240713517  0.73848372     0.000000       0.0000 0.0028
##  [21,] -206.2125821425 26.20824599  -258.268490    -156.1275 1.0000
##  [22,]   -0.2400780156  2.92652668     0.000000       0.0000 0.0108
##  [23,]   -0.0060265519  1.01215940     0.000000       0.0000 0.0060
##  [24,]   -0.0685162071  1.35843746     0.000000       0.0000 0.0048
##  [25,]   -0.0209456752  0.97375569     0.000000       0.0000 0.0044
##  [26,]   -0.0210436502  0.53231731     0.000000       0.0000 0.0020
##  [27,]   -0.1527270724  1.92769929     0.000000       0.0000 0.0088
##  [28,]   -0.0039308541  0.72973243     0.000000       0.0000 0.0028
##  [29,]   -0.1737128045  2.75426473     0.000000       0.0000 0.0084
##  [30,]   -0.0679881334  1.34286321     0.000000       0.0000 0.0060
##  [31,]   -0.0146431497  0.67951589     0.000000       0.0000 0.0016
##  [32,]   -0.0385608213  0.85166799     0.000000       0.0000 0.0028
##  [33,]   -0.0290325606  0.83963683     0.000000       0.0000 0.0024
##  [34,]    0.0395633599  1.29349388     0.000000       0.0000 0.0028
##  [35,]    0.0393328251  2.22029741     0.000000       0.0000 0.0044
##  [36,]   -0.0646843744  1.24873801     0.000000       0.0000 0.0040
##  [37,]   -0.0081690735  0.31009016     0.000000       0.0000 0.0020
##  [38,]    0.0831086681  2.17465477     0.000000       0.0000 0.0040
##  [39,]    0.0462511699  1.93628092     0.000000       0.0000 0.0048
##  [40,]   -0.7048485681  6.26268221     0.000000       0.0000 0.0196
##  [41,]   -0.0747840946  1.28751970     0.000000       0.0000 0.0052
##  [42,]    0.0056663532  1.02205045     0.000000       0.0000 0.0052
##  [43,]   -0.0421927788  1.23241282     0.000000       0.0000 0.0032
##  [44,]    0.0268868998  0.85263548     0.000000       0.0000 0.0044
##  [45,]   -0.0185501837  1.02526798     0.000000       0.0000 0.0052
##  [46,]   -0.0073991280  0.29798903     0.000000       0.0000 0.0020
##  [47,]   -0.4367164323  4.88907097     0.000000       0.0000 0.0132
##  [48,]   -0.2464188571  3.48468772     0.000000       0.0000 0.0092
##  [49,]   -0.0751657192  1.48026938     0.000000       0.0000 0.0048
##  [50,]   -0.0685231016  1.44260735     0.000000       0.0000 0.0068
##  [51,]   -0.1706076186  2.40739716     0.000000       0.0000 0.0080
##  [52,]   -0.0643325613  1.43996719     0.000000       0.0000 0.0068
##  [53,]    0.0093569095  1.12834029     0.000000       0.0000 0.0020
##  [54,]   -0.0641256378  1.32544801     0.000000       0.0000 0.0048
##  [55,]   -0.0365915921  0.84233854     0.000000       0.0000 0.0048
##  [56,]    0.0168849882  0.48747522     0.000000       0.0000 0.0016
##  [57,]    0.0314640681  1.04552688     0.000000       0.0000 0.0040
##  [58,]   -0.0099131355  0.57978774     0.000000       0.0000 0.0032
##  [59,]   -0.0135252355  0.79034667     0.000000       0.0000 0.0036
##  [60,]    0.0317636479  1.14633576     0.000000       0.0000 0.0028
##  [61,]   -0.0308231854  0.70204152     0.000000       0.0000 0.0040
##  [62,]   -0.0173088455  0.73155228     0.000000       0.0000 0.0048
##  [63,]    0.0088399422  0.78218889     0.000000       0.0000 0.0020
##  [64,]   -0.0111968101  0.92875878     0.000000       0.0000 0.0024
##  [65,]   -0.0802219868  1.74725609     0.000000       0.0000 0.0068
##  [66,]   -0.0242938964  1.04773993     0.000000       0.0000 0.0060
##  [67,]   -0.0163328246  0.85318793     0.000000       0.0000 0.0032
##  [68,]   -0.0310902955  1.51310037     0.000000       0.0000 0.0048
##  [69,]   -0.0153893417  0.44639080     0.000000       0.0000 0.0028
##  [70,]   -0.0489179275  0.93122160     0.000000       0.0000 0.0048
##  [71,]   -0.0150699602  1.27635701     0.000000       0.0000 0.0032
##  [72,]   -0.0037215936  1.21758508     0.000000       0.0000 0.0044
##  [73,]    0.0417965314  1.37402199     0.000000       0.0000 0.0040
##  [74,]   -0.0604374949  1.03782246     0.000000       0.0000 0.0052
##  [75,]    0.0135998361  1.31508411     0.000000       0.0000 0.0040
##  [76,]    0.0130161928  0.70111767     0.000000       0.0000 0.0044
##  [77,]    0.0103494597  0.34362680     0.000000       0.0000 0.0012
##  [78,]   -0.0647566796  1.53315098     0.000000       0.0000 0.0032
##  [79,]   -0.0081710590  0.51715691     0.000000       0.0000 0.0020
##  [80,]   -0.0599088114  1.51715685     0.000000       0.0000 0.0052
##  [81,]   -0.0078597781  0.97252950     0.000000       0.0000 0.0028
##  [82,]   -0.0339790002  1.41162809     0.000000       0.0000 0.0040
##  [83,]    0.0077999691  1.15538645     0.000000       0.0000 0.0048
##  [84,]   -0.0081781041  0.45389053     0.000000       0.0000 0.0020
##  [85,]   -0.0037911698  0.37078711     0.000000       0.0000 0.0036
##  [86,]   -0.0193299399  1.37800858     0.000000       0.0000 0.0040
##  [87,]   -0.0330055935  0.67374076     0.000000       0.0000 0.0040
##  [88,]   -0.0655375443  1.05462115     0.000000       0.0000 0.0060
##  [89,]   -0.0136056057  1.22686092     0.000000       0.0000 0.0040
##  [90,]   -0.0119416174  0.59901714     0.000000       0.0000 0.0028
##  [91,]    0.0231621094  1.19860367     0.000000       0.0000 0.0052
##  [92,]    0.0345869227  1.68781124     0.000000       0.0000 0.0040
##  [93,]    0.0372718154  1.63730836     0.000000       0.0000 0.0024
##  [94,]    0.0829768349  1.62783643     0.000000       0.0000 0.0052
##  [95,]    0.0342466715  1.25574668     0.000000       0.0000 0.0032
##  [96,]    0.0545790259  2.25461736     0.000000       0.0000 0.0056
##  [97,]   -0.0681226919  1.39864591     0.000000       0.0000 0.0044
##  [98,]   -0.0853015186  1.71880044     0.000000       0.0000 0.0056
##  [99,]   -0.1248130799  1.96110500     0.000000       0.0000 0.0072
## [100,]   -0.1350835169  2.00055431     0.000000       0.0000 0.0068
## [101,]   -0.0568126291  1.13890466     0.000000       0.0000 0.0056
## [102,]   -0.1411941369  2.21763113     0.000000       0.0000 0.0076
## [103,]   -0.0100778091  0.91575867     0.000000       0.0000 0.0028
## [104,]   -0.0458850174  1.07010848     0.000000       0.0000 0.0032
## [105,]   -0.0382695724  1.27550602     0.000000       0.0000 0.0048
## [106,]   -0.0326511904  1.74845779     0.000000       0.0000 0.0032
## [107,]    0.0890972067  2.13571095     0.000000       0.0000 0.0048
## [108,]    0.0256476956  0.70920253     0.000000       0.0000 0.0036
## [109,]    0.0859596759  2.01690190     0.000000       0.0000 0.0052
## [110,]    0.1538768309  2.94232126     0.000000       0.0000 0.0076
## [111,]   -0.0155355295  0.38530975     0.000000       0.0000 0.0028
## [112,]   -0.0225891609  0.84800140     0.000000       0.0000 0.0040
## [113,]   -0.0113179570  1.13673519     0.000000       0.0000 0.0024
## [114,]   -0.0040659037  0.42620757     0.000000       0.0000 0.0020
## [115,]   -0.0185040169  0.98300384     0.000000       0.0000 0.0040
## [116,]   -0.0081916329  1.10477075     0.000000       0.0000 0.0032
## [117,]    0.0563032783  2.51520445     0.000000       0.0000 0.0036
## [118,]    0.0257777950  1.51074004     0.000000       0.0000 0.0028
## [119,]   -0.0837748668  1.76235527     0.000000       0.0000 0.0052
## [120,]   -0.0031752076  1.47242039     0.000000       0.0000 0.0064
## [121,]   -0.0100218670  0.41453868     0.000000       0.0000 0.0024
## [122,]   -0.0492681330  1.18682902     0.000000       0.0000 0.0056
## [123,]    0.0476624665  1.75060435     0.000000       0.0000 0.0028
## [124,]   -0.0139606635  1.12981800     0.000000       0.0000 0.0044
## [125,]    0.0620216190  3.11517448     0.000000       0.0000 0.0064
## [126,]   -0.0243090547  0.86234170     0.000000       0.0000 0.0036
## [127,]   -0.0296081023  0.88956426     0.000000       0.0000 0.0024
## [128,]   -0.0683341929  1.19094047     0.000000       0.0000 0.0048
## [129,]   -0.0438917810  1.22138127     0.000000       0.0000 0.0040
## [130,]    0.0109881930  1.64837552     0.000000       0.0000 0.0044
## [131,]   -0.0975372430  1.71058274     0.000000       0.0000 0.0060
## [132,]   -0.0833101538  1.38186576     0.000000       0.0000 0.0048
## [133,]    0.0217145027  1.56957346     0.000000       0.0000 0.0024
## [134,]    0.1565963002  3.07731236     0.000000       0.0000 0.0068
## [135,]   -0.0141679950  0.90494094     0.000000       0.0000 0.0044
## [136,]   -0.0341214078  1.09426466     0.000000       0.0000 0.0060
## [137,]   -0.0774575566  1.45802041     0.000000       0.0000 0.0060
## [138,]   -0.0937953580  1.74557848     0.000000       0.0000 0.0036
## [139,]   -0.0459412811  1.72834446     0.000000       0.0000 0.0056
## [140,]   -0.0741696912  1.26413737     0.000000       0.0000 0.0040
## [141,]   -0.0401157553  0.96875988     0.000000       0.0000 0.0036
## [142,]   -0.0211964361  0.63073354     0.000000       0.0000 0.0028
## [143,]   -0.0065425294  1.43646148     0.000000       0.0000 0.0056
## [144,]   -0.0530046258  1.38950291     0.000000       0.0000 0.0044
## [145,]    0.0763850573  2.11020536     0.000000       0.0000 0.0036
## [146,]    0.8366987239  7.59305655     0.000000       0.0000 0.0156
## [147,]   -0.0721040882  1.76598394     0.000000       0.0000 0.0044
## [148,]   -0.0478081809  0.91629650     0.000000       0.0000 0.0052
## [149,]   -0.0791618538  1.55322545     0.000000       0.0000 0.0064
## [150,]   -0.0017363071  0.98007204     0.000000       0.0000 0.0028
## [151,]   -0.0578144310  1.22473842     0.000000       0.0000 0.0052
## [152,]   -0.1417508344  2.35505138     0.000000       0.0000 0.0076
## [153,]   -0.0914211996  1.92121996     0.000000       0.0000 0.0032
## [154,]   -0.1264518021  1.78160059     0.000000       0.0000 0.0072
## [155,]   -0.4112049438  4.73925657     0.000000       0.0000 0.0112
## [156,]   -0.0510399421  1.52460439     0.000000       0.0000 0.0052
## [157,]   -0.0379945417  0.73935559     0.000000       0.0000 0.0052
## [158,]   -0.0536358075  1.04032248     0.000000       0.0000 0.0056
## [159,]    0.0175178080  0.63346203     0.000000       0.0000 0.0024
## [160,]   -0.0526341494  0.94412746     0.000000       0.0000 0.0044
## [161,]   -0.0496292658  1.12332379     0.000000       0.0000 0.0036
## [162,]   -0.0389468292  1.07211710     0.000000       0.0000 0.0048
## [163,]   -0.0038053419  0.68410632     0.000000       0.0000 0.0040
## [164,]   -0.1119695336  2.09416897     0.000000       0.0000 0.0052
## [165,]   -0.0199873763  0.44095144     0.000000       0.0000 0.0036
## [166,]   -0.0335560105  1.60842646     0.000000       0.0000 0.0048
## [167,]   -0.0535640728  1.19046137     0.000000       0.0000 0.0052
## [168,]    2.4263986680 14.21792788     0.000000      60.6956 0.0344
## [169,]   -0.0658748298  1.09733380     0.000000       0.0000 0.0044
## [170,]   -0.0266425913  1.42176979     0.000000       0.0000 0.0036
## [171,]    0.2132715055  4.19361305     0.000000       0.0000 0.0072
## [172,]    0.8483790018  9.14384700     0.000000       0.0000 0.0140
## [173,]    0.1461777231  3.43567766     0.000000       0.0000 0.0048
## [174,]    0.0253720953  1.39536427     0.000000       0.0000 0.0040
## [175,]    0.0062901303  0.46848216     0.000000       0.0000 0.0020
## [176,]   -0.0830855379  1.64099854     0.000000       0.0000 0.0056
## [177,]   -0.0746604394  1.65100634     0.000000       0.0000 0.0048
## [178,]   -0.0462151263  1.26573502     0.000000       0.0000 0.0028
## [179,]   -0.0905022910  1.87573119     0.000000       0.0000 0.0036
## [180,]   -0.0780102372  1.49198534     0.000000       0.0000 0.0056
## [181,]   -0.1072322085  1.85253595     0.000000       0.0000 0.0068
## [182,]   -0.0196062320  0.92669284     0.000000       0.0000 0.0036
## [183,]   -0.0055348192  0.38098076     0.000000       0.0000 0.0012
## [184,]   -0.0265231893  0.62921556     0.000000       0.0000 0.0028
## [185,]    0.0202589158  1.15507769     0.000000       0.0000 0.0032
## [186,]   -0.0104993752  0.69884696     0.000000       0.0000 0.0016
## [187,]   -0.0055486100  1.28275299     0.000000       0.0000 0.0040
## [188,]   -0.0061700355  0.64651323     0.000000       0.0000 0.0024
## [189,]   -0.0159108685  0.36803014     0.000000       0.0000 0.0020
## [190,]   -0.0012436617  0.04412822     0.000000       0.0000 0.0008
## [191,]   -0.0270561219  0.95700034     0.000000       0.0000 0.0032
## [192,]    0.0022670245  0.75033271     0.000000       0.0000 0.0044
## [193,]   -0.1204012874  2.37639132     0.000000       0.0000 0.0052
## [194,]    0.0028728263  0.09170568     0.000000       0.0000 0.0012
## [195,]   -0.1397801403  2.03552727     0.000000       0.0000 0.0060
## [196,]   -0.0594247964  1.21355377     0.000000       0.0000 0.0040
## [197,]    0.0091917121  0.54099345     0.000000       0.0000 0.0040
## [198,]   -0.0706524061  1.25733830     0.000000       0.0000 0.0064
## [199,]   -0.0225358292  0.75018052     0.000000       0.0000 0.0024
## [200,]   -0.0879458405  1.66080414     0.000000       0.0000 0.0036
## [201,]   -0.0264680074  0.54489285     0.000000       0.0000 0.0036
## [202,]   -0.0215886925  0.52225648     0.000000       0.0000 0.0032
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## [448,]   -1.1684377187 14.87524299     0.000000       0.0000 0.0108
## [449,]   -0.0413877577  1.44730591     0.000000       0.0000 0.0048
## [450,]   -0.1660490284  4.23382749     0.000000       0.0000 0.0076
## [451,]    0.0561049194  3.44910563     0.000000       0.0000 0.0056
## [452,]   -0.0019084188  1.98210127     0.000000       0.0000 0.0040
## [453,]    0.1009729034  3.22707879     0.000000       0.0000 0.0036
## [454,]    0.0209852022  3.32955154     0.000000       0.0000 0.0068
## [455,]    0.0762255493  3.84228069     0.000000       0.0000 0.0064
## [456,]   -0.0971113219  2.97699665     0.000000       0.0000 0.0068
## [457,]   -0.0310015085  1.87247291     0.000000       0.0000 0.0044
## [458,]   -0.0636571493  1.28874742     0.000000       0.0000 0.0040
## [459,]   -0.4385013497  9.01948724     0.000000       0.0000 0.0060
## [460,]   -0.1920543864  3.05573264     0.000000       0.0000 0.0104
## [461,]   -0.0224233185  0.79212889     0.000000       0.0000 0.0040
## [462,]   -0.0956529169  1.97164798     0.000000       0.0000 0.0056
## [463,]   -0.0544165420  1.42112521     0.000000       0.0000 0.0060
## [464,]   -0.0371015210  0.92565641     0.000000       0.0000 0.0024
## [465,]    0.1594103344  3.42218892     0.000000       0.0000 0.0052
## [466,]   -0.0249949332  1.56330363     0.000000       0.0000 0.0052
## [467,]   -0.0676165497  2.04419623     0.000000       0.0000 0.0044
## [468,]   -0.0344458740  2.75752751     0.000000       0.0000 0.0052
## [469,]    0.1340502283  3.52213530     0.000000       0.0000 0.0052
## [470,]   -0.0027540114  2.33257555     0.000000       0.0000 0.0044
## [471,]   -0.5528728210 13.68734025     0.000000       0.0000 0.0092
## [472,]   -0.0072356006  1.88776714     0.000000       0.0000 0.0060
## [473,]    0.0568551774  3.15113893     0.000000       0.0000 0.0068
## [474,]    0.3197411612  4.92685429     0.000000       0.0000 0.0064
## [475,]   -0.0599999554  4.05363615     0.000000       0.0000 0.0064
## [476,]    0.0399713519  1.92243422     0.000000       0.0000 0.0064
## [477,]   -0.1946271769  5.08178599     0.000000       0.0000 0.0068
## [478,]    0.2053638027  4.49810049     0.000000       0.0000 0.0064
## [479,]   -0.1143120016  1.85425982     0.000000       0.0000 0.0052
## [480,]    0.0864254678  2.06905528     0.000000       0.0000 0.0040
## [481,]   -0.0626801171  1.21338238     0.000000       0.0000 0.0048
## [482,]   -0.0149928847  2.89093276     0.000000       0.0000 0.0064
## [483,]   -0.0015363306  1.66727961     0.000000       0.0000 0.0056
## [484,]    0.0138256908  0.77921363     0.000000       0.0000 0.0032
## [485,]   -0.0032621487  0.73260621     0.000000       0.0000 0.0040
## [486,]   -0.0869697473  2.18487078     0.000000       0.0000 0.0052
## [487,]   -0.0209197386  0.91531522     0.000000       0.0000 0.0068
## [488,]    0.0024690824  0.69941692     0.000000       0.0000 0.0032
## [489,]   -0.0191977486  0.84478395     0.000000       0.0000 0.0040
## [490,]   -0.0764790506  3.10678643     0.000000       0.0000 0.0036
## [491,]   -0.3774899801  6.52631279     0.000000       0.0000 0.0072
## [492,]   -0.0822544251  1.69072960     0.000000       0.0000 0.0044
## [493,]    0.0219511748  2.06699779     0.000000       0.0000 0.0076
## [494,]   -1.3931775733 16.41039608     0.000000       0.0000 0.0136
## [495,]    0.0357057805  2.59084441     0.000000       0.0000 0.0052
## [496,]    0.0786749334  3.06107278     0.000000       0.0000 0.0064
## [497,]   -0.8186617305 11.55335230     0.000000       0.0000 0.0120
## [498,]   -0.0271088674  3.98492181     0.000000       0.0000 0.0060
## [499,]   -0.0693145725  1.73758934     0.000000       0.0000 0.0048
## [500,]   -0.0783677760  2.05654514     0.000000       0.0000 0.0072
## [501,]   -1.7874217817 17.66793279     0.000000       0.0000 0.0168
## [502,]    0.0993739409  2.66601697     0.000000       0.0000 0.0040
## [503,]   -0.0173530886  0.79244463     0.000000       0.0000 0.0036
## [504,]   -0.0261155640  0.72996381     0.000000       0.0000 0.0044
## [505,]   -0.1534551283  4.98297432     0.000000       0.0000 0.0036
## [506,]   -0.0111187382  2.56189592     0.000000       0.0000 0.0044
## [507,]   -0.0416920611  1.18824411     0.000000       0.0000 0.0060
## [508,]   -0.0221239126  0.60856395     0.000000       0.0000 0.0016
## [509,]    0.0920051281  3.62639153     0.000000       0.0000 0.0052
## [510,]   -0.0377847727  1.25306767     0.000000       0.0000 0.0064
## [511,]   -0.0033705552  0.74909325     0.000000       0.0000 0.0032
## [512,]    0.0001585552  0.61861619     0.000000       0.0000 0.0032
## [513,]   -0.0634232836  2.56986350     0.000000       0.0000 0.0060
## [514,]   -0.2436404617  4.53997751     0.000000       0.0000 0.0060
## [515,]   -0.5348147943  8.39557492     0.000000       0.0000 0.0084
## [516,]    0.0216736304  2.80958135     0.000000       0.0000 0.0060
## [517,]   -1.6632661810 17.68998507     0.000000       0.0000 0.0136
## [518,]   -0.0529475344  3.10973372     0.000000       0.0000 0.0064
## [519,]   -0.0395821471  1.21521596     0.000000       0.0000 0.0028
## [520,]   -0.5011248055  8.22073898     0.000000       0.0000 0.0088
## [521,]    0.1098798910  3.66228908     0.000000       0.0000 0.0060
## [522,]   -0.1008348364  1.49920103     0.000000       0.0000 0.0060
## [523,]   -0.1544545616  4.29375268     0.000000       0.0000 0.0052
## [524,]   -0.6050696540  9.19849273     0.000000       0.0000 0.0080
## [525,]    0.0553315481  3.46103161     0.000000       0.0000 0.0048
## [526,]   -0.0331841462  1.70608733     0.000000       0.0000 0.0052
## [527,]   -0.0322305075  0.79746773     0.000000       0.0000 0.0040
## [528,]   -0.0315808385  2.27931479     0.000000       0.0000 0.0040
## [529,]   -0.0303297624  0.74947793     0.000000       0.0000 0.0052
## [530,]   -0.0244831560  0.81612537     0.000000       0.0000 0.0040
## [531,]   -0.0171973202  0.69287401     0.000000       0.0000 0.0052
## [532,]   -0.0535350198  1.26200828     0.000000       0.0000 0.0048
## [533,]   -0.0840389361  1.46618638     0.000000       0.0000 0.0072
## [534,]   -0.0555432711  0.90184117     0.000000       0.0000 0.0056
## [535,]   -0.0131964297  0.71956311     0.000000       0.0000 0.0024
## [536,]   -0.0617746924  1.54315742     0.000000       0.0000 0.0036
## [537,]   -0.0604468006  2.57669800     0.000000       0.0000 0.0072
## [538,]   -0.1294909363  2.46721901     0.000000       0.0000 0.0052
## [539,]    0.9645270332 12.70467034     0.000000       0.0000 0.0136
## [540,]   -0.8992885626 13.44496938     0.000000       0.0000 0.0088
## [541,]    0.4192617205  6.61964339     0.000000       0.0000 0.0084
## [542,]    0.0685117096  2.03867630     0.000000       0.0000 0.0040
## [543,]    0.0070458745  1.53437951     0.000000       0.0000 0.0036
## [544,]    0.2543831064  4.52719936     0.000000       0.0000 0.0056
## [545,]    0.0299019565  2.33696978     0.000000       0.0000 0.0056
## [546,]    0.1277032008  4.64107034     0.000000       0.0000 0.0092
## [547,]   -0.3376420674  6.95774616     0.000000       0.0000 0.0076
## [548,]    0.0721325110  2.34683262     0.000000       0.0000 0.0044
## [549,]    0.0396225240  3.47258259     0.000000       0.0000 0.0072
## [550,]   -0.0057769753  0.89114427     0.000000       0.0000 0.0040
## [551,]   -0.2089964565  6.23160726     0.000000       0.0000 0.0072
## [552,]   -0.0153466750  1.94382219     0.000000       0.0000 0.0064
## [553,]   -0.3840184693  4.21333517     0.000000       0.0000 0.0116
## [554,]   -0.0853845059  1.65713661     0.000000       0.0000 0.0064
## [555,]   -0.0381893524  2.32756292     0.000000       0.0000 0.0052
## [556,]    0.0058135667  1.00191344     0.000000       0.0000 0.0032
## [557,]   -0.0203855613  1.20983353     0.000000       0.0000 0.0060
## [558,]   -0.0189918893  1.60001037     0.000000       0.0000 0.0036
## [559,]   -0.0089629902  2.87420987     0.000000       0.0000 0.0056
## [560,]   -0.1511731417  2.68905092     0.000000       0.0000 0.0060
## [561,]    0.0413147042  1.65982820     0.000000       0.0000 0.0020
## [562,]    0.2842180510  6.45290394     0.000000       0.0000 0.0064
## [563,]   -1.3702638683 16.95348279     0.000000       0.0000 0.0132
## [564,]    0.0812658378  2.90535324     0.000000       0.0000 0.0060
## [565,]   -0.0709405443  1.69284999     0.000000       0.0000 0.0048
## [566,]   -0.0247247522  0.88431030     0.000000       0.0000 0.0040
## [567,]    0.1916040076  5.05463367     0.000000       0.0000 0.0076
## [568,]   -0.1123323611  5.02482684     0.000000       0.0000 0.0092
## [569,]   -1.6653037160 17.56936713     0.000000       0.0000 0.0148
## [570,]   -0.0753005302  2.06343194     0.000000       0.0000 0.0048
## [571,]    0.0843691606  2.28379843     0.000000       0.0000 0.0064
## [572,]    0.0542162420  2.14259018     0.000000       0.0000 0.0056
## [573,]    0.0596853297  2.72078323     0.000000       0.0000 0.0060
## [574,]    0.0515983555  2.51716790     0.000000       0.0000 0.0040
## [575,]   -0.0740776807  1.55388179     0.000000       0.0000 0.0048
## [576,]   -0.0365334227  0.84504453     0.000000       0.0000 0.0044
## [577,]   -0.0583725551  1.26575342     0.000000       0.0000 0.0036
## [578,]   -0.0685488786  1.99573504     0.000000       0.0000 0.0040
## [579,]    0.0193013700  2.32850372     0.000000       0.0000 0.0048
## [580,]   -0.1111904840  2.26730087     0.000000       0.0000 0.0060
## [581,]   -0.0984716471  1.52846880     0.000000       0.0000 0.0056
## [582,]   -0.0788602479  1.64577714     0.000000       0.0000 0.0060
## [583,]    0.0776536429  2.82006042     0.000000       0.0000 0.0036
## [584,]    0.0634527403  2.76837096     0.000000       0.0000 0.0056
## [585,]   -0.0646800360  1.43685882     0.000000       0.0000 0.0056
## [586,]   -0.0462468819  5.72460017     0.000000       0.0000 0.0076
## [587,]    0.0310824768  1.45195070     0.000000       0.0000 0.0020
## [588,]    0.2625842175  4.88583723     0.000000       0.0000 0.0076
## [589,]   -0.0600922962  1.57369833     0.000000       0.0000 0.0048
## [590,]    0.0085786886  3.59896153     0.000000       0.0000 0.0080
## [591,]   -0.1476379811  3.92266498     0.000000       0.0000 0.0060
## [592,]    0.0821139875  3.49696612     0.000000       0.0000 0.0068
## [593,]   -0.1020889230  2.27530753     0.000000       0.0000 0.0064
## [594,]    0.0428747086  2.14784732     0.000000       0.0000 0.0052
## [595,]   -0.1047010156  6.49800137     0.000000       0.0000 0.0080
## [596,]   -0.0432069578  0.96983860     0.000000       0.0000 0.0032
## [597,]    0.1575885874  4.45612680     0.000000       0.0000 0.0052
## [598,]    0.4815410140  6.84389507     0.000000       0.0000 0.0072
## [599,]   -0.0233258251  1.17038753     0.000000       0.0000 0.0060
## [600,]    0.0610965138  1.90413243     0.000000       0.0000 0.0040
## [601,]    0.0421500137  2.12151170     0.000000       0.0000 0.0048
## [602,]    0.0500769320  2.17830926     0.000000       0.0000 0.0048
## [603,]   -0.1675848490  2.42688825     0.000000       0.0000 0.0084
## [604,]   -0.0379813336  1.03049234     0.000000       0.0000 0.0048
## [605,]   -0.0593494680  2.76244824     0.000000       0.0000 0.0064
## [606,]   -0.0108868982  1.30784658     0.000000       0.0000 0.0048
## [607,]   -0.1139151105  2.35880065     0.000000       0.0000 0.0060
## [608,]   -0.0263281383  1.20242967     0.000000       0.0000 0.0056
## [609,]   -0.2614575429  7.39902488     0.000000       0.0000 0.0064
## [610,]   -0.3503280808  6.13296607     0.000000       0.0000 0.0068
## [611,]    0.1173816024  3.68735802     0.000000       0.0000 0.0048
## [612,]   -0.2424616581  4.59740137     0.000000       0.0000 0.0076
## [613,]    0.0444051720  3.01405177     0.000000       0.0000 0.0056
## [614,]   -1.4777863482 15.47448634     0.000000       0.0000 0.0156
## [615,]   -0.0302196290  1.42166587     0.000000       0.0000 0.0044
## [616,]   -0.1564661194  4.99367869     0.000000       0.0000 0.0092
## [617,]   -0.1608200267  4.29557640     0.000000       0.0000 0.0064
## [618,]    0.0491568295  2.59896675     0.000000       0.0000 0.0028
## [619,]   -0.0196546874  1.47712036     0.000000       0.0000 0.0044
## [620,]   -0.3626987193  8.74035295     0.000000       0.0000 0.0080
## [621,]   -0.8790074235 10.83180971     0.000000       0.0000 0.0104
## [622,]   -0.0672634759  1.56165971     0.000000       0.0000 0.0056
## [623,]   -0.0141782621  1.08791902     0.000000       0.0000 0.0048
## [624,]   -0.1839401771  3.22835543     0.000000       0.0000 0.0076
## [625,]   -0.1580815176  2.80378448     0.000000       0.0000 0.0080
## [626,]   -0.2257300669  3.86171148     0.000000       0.0000 0.0068
## [627,]   -0.0355392306  1.27124146     0.000000       0.0000 0.0024
## [628,]    0.0120803067  2.15798267     0.000000       0.0000 0.0036
## [629,]   -0.0828119175  2.73008678     0.000000       0.0000 0.0056
## [630,]   -0.0267016713  1.71251306     0.000000       0.0000 0.0060
## [631,]   -0.0592281892  5.20616797     0.000000       0.0000 0.0064
## [632,]   -0.5885150720  9.05423577     0.000000       0.0000 0.0128
## [633,]   -0.0305801989  0.89603945     0.000000       0.0000 0.0024
## [634,]    0.2387725098  4.70764664     0.000000       0.0000 0.0080
## [635,]   -0.1627806885  4.49210520     0.000000       0.0000 0.0044
## [636,]   -0.0617112089  2.54637993     0.000000       0.0000 0.0052
## [637,]    0.0350711713  3.58469728     0.000000       0.0000 0.0044
## [638,]    0.2095100629  4.11866991     0.000000       0.0000 0.0052
## [639,]   -0.0342798600  1.33261491     0.000000       0.0000 0.0024
## [640,]   -0.0084099888  0.84954552     0.000000       0.0000 0.0028
## [641,]   -0.1385948444  3.87861364     0.000000       0.0000 0.0060
## [642,]    0.0293340062  0.81526387     0.000000       0.0000 0.0028
## [643,]   -0.6685166101 11.61380435     0.000000       0.0000 0.0072
## [644,]   -0.0682290560  1.75600204     0.000000       0.0000 0.0052
## [645,]    0.0092579167  1.80028140     0.000000       0.0000 0.0048
## [646,]   -0.0273464221  0.92217265     0.000000       0.0000 0.0036
## [647,]   -0.0854202641  2.43718698     0.000000       0.0000 0.0060
## [648,]    0.0459801096  2.31289800     0.000000       0.0000 0.0032
## [649,]   -0.1096894450  1.39330213     0.000000       0.0000 0.0084
## [650,]   -0.2417299673  3.27174611     0.000000       0.0000 0.0080
## [651,]    0.2042338004  4.44568737     0.000000       0.0000 0.0056
## [652,]   -0.1766229152  2.66261031     0.000000       0.0000 0.0076
## [653,]    0.0134780550  2.23058113     0.000000       0.0000 0.0036
## [654,]    0.1556819609  5.13217222     0.000000       0.0000 0.0072
## [655,]   -0.3363839413  8.77449805     0.000000       0.0000 0.0100
## [656,]   -0.0685256950  1.87948726     0.000000       0.0000 0.0072
## [657,]    0.0717129330  2.91825108     0.000000       0.0000 0.0068
## [658,]   -0.0721913257  1.66795064     0.000000       0.0000 0.0036
## [659,]   -0.0192637629  2.90982126     0.000000       0.0000 0.0044
## [660,]   -0.0902501130  2.35798575     0.000000       0.0000 0.0040
## [661,]    0.0024061770  2.38168227     0.000000       0.0000 0.0040
## [662,]    0.0193289832  2.71049490     0.000000       0.0000 0.0064
## [663,]    0.2552594658  4.96866040     0.000000       0.0000 0.0060
## [664,]   -0.0359991062  1.08722342     0.000000       0.0000 0.0040
## [665,]   -0.0044164597  0.78245187     0.000000       0.0000 0.0044
## [666,]   -0.3611609014  7.92386045     0.000000       0.0000 0.0080
## [667,]    0.0073752164  1.37813136     0.000000       0.0000 0.0052
## [668,]   -0.0385130085  0.81978164     0.000000       0.0000 0.0040
## [669,]   -0.0551265379  1.54411194     0.000000       0.0000 0.0040
## [670,]   -0.0557528777  1.85029759     0.000000       0.0000 0.0048
## [671,]    0.0907486359  2.10358646     0.000000       0.0000 0.0040
## [672,]   -0.1615316574  2.54481808     0.000000       0.0000 0.0084
## [673,]   -0.0858680825  1.35458873     0.000000       0.0000 0.0076
## [674,]   -0.0525483042  1.83533256     0.000000       0.0000 0.0052
## [675,]   -0.1448204010  2.79079210     0.000000       0.0000 0.0076
## [676,]   -0.0371730028  1.37144680     0.000000       0.0000 0.0052
## [677,]    0.0950271444  3.51175568     0.000000       0.0000 0.0056
## [678,]    0.0034452835  5.18832726     0.000000       0.0000 0.0060
## [679,]    0.1106510096  3.18050479     0.000000       0.0000 0.0028
## [680,]    0.0668577817  1.94929540     0.000000       0.0000 0.0048
## [681,]   -0.0329033077  0.91556795     0.000000       0.0000 0.0036
## [682,]    0.0199787182  2.48599485     0.000000       0.0000 0.0068
## [683,]   -0.0581867326  3.29939382     0.000000       0.0000 0.0084
## [684,]    0.0852966000  3.23355938     0.000000       0.0000 0.0084
## [685,]   -0.1779685780  3.67182750     0.000000       0.0000 0.0068
## [686,]    0.1297996562  3.45998648     0.000000       0.0000 0.0044
## [687,]   -0.1007538099  1.67679173     0.000000       0.0000 0.0056
## [688,]   -0.0402634947  0.93569888     0.000000       0.0000 0.0040
## [689,]    0.0513569057  2.47398340     0.000000       0.0000 0.0040
## [690,]   -0.0045080349  1.36656737     0.000000       0.0000 0.0028
## [691,]   -0.1401440689  2.30575600     0.000000       0.0000 0.0052
## [692,]   -0.0527173460  1.37532287     0.000000       0.0000 0.0032
## [693,]    0.1029519464  3.11296613     0.000000       0.0000 0.0044

3.2.4 Predict fitted values for each individual

pred.npb2 <- predict(fit.npb2)
fittedvals2 <- pred.npb2$fitted.vals

3.2.5 Plot predicted outcomes against “measured” outcomes

plot(fittedvals2, Y)
abline(a = 0, b = 1, col = "red")

4 Linear models for each predictor

4.1 Screening the exposures

Here I’m going to loop through some linear regression models to see if anything shows up here. Remember that the exposure and covariates have all been scaled.

The standard deviation of the mean_o3 variable is 3.14 ppb

lm_results <- data.frame()

for(i in 1:length(colnames(X.scaled))) {
  lm_df <- as.data.frame(cbind(Y, X.scaled[,i], W.scaled2))
  names(lm_df)[2] <- colnames(X.scaled)[i]
  
  ad_lm <- lm(birth_weight ~ ., data = lm_df)
  
  temp <- data.frame(exp = colnames(X.scaled)[i],
                     beta = summary(ad_lm)$coefficients[2,1],
                     beta.se = summary(ad_lm)$coefficients[2,2],
                     p.value = summary(ad_lm)$coefficients[2,4])
  temp$lcl <- temp$beta - 1.96*temp$beta.se
  temp$ucl <- temp$beta + 1.96*temp$beta.se
  lm_results <- bind_rows(lm_results, temp)
  rm(temp)
}

lm_results
write_csv(lm_results, here::here("Results", "LM_Effects_Birth_Weight_v4c.csv"))

5 Linear model with the ozone and temperature predictors

The mean and standard deviation of the mean_o3 variable are 48.11 (3.14) ppb The mean and standard deviation of the mean_temp variable is 52.67 (4.69) degrees F

lm_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(lm_df)
##  [1] "birth_weight"  "mean_o3"       "mean_temp"     "lat"          
##  [5] "lon"           "lat_lon_int"   "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
#names(lm_df)[2] <- "mean_o3"

head(lm_df)
bw_lm <- lm(birth_weight ~ mean_o3 + mean_temp + mean_o3*mean_temp +
              lat + lon + lat_lon_int +
              ed_no_hs + ed_hs + ed_aa + ed_4yr + 
              low_bmi + ovwt_bmi + obese_bmi + 
              concep_spring + concep_summer + concep_fall +
              concep_2010 + concep_2011 + concep_2012 + concep_2013 +
              maternal_age + any_smoker + smokeSH + 
              mean_cpss + mean_epsd + male,
              data = lm_df)

summary(bw_lm)
## 
## Call:
## lm(formula = birth_weight ~ mean_o3 + mean_temp + mean_o3 * mean_temp + 
##     lat + lon + lat_lon_int + ed_no_hs + ed_hs + ed_aa + ed_4yr + 
##     low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer + 
##     concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 + 
##     maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd + 
##     male, data = lm_df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1659.22  -309.97    29.09   320.30  1471.90 
## 
## Coefficients:
##                    Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)        2690.378    504.745   5.330          0.000000160 ***
## mean_o3            -202.202     84.710  -2.387               0.0174 *  
## mean_temp           150.584     86.192   1.747               0.0813 .  
## lat               -3309.480  26030.095  -0.127               0.8989    
## lon                1517.986  12042.902   0.126               0.8998    
## lat_lon_int       -3949.994  30989.410  -0.127               0.8986    
## ed_no_hs            295.170    124.072   2.379               0.0178 *  
## ed_hs               280.067    118.869   2.356               0.0189 *  
## ed_aa               153.791    115.352   1.333               0.1832    
## ed_4yr              218.451    122.524   1.783               0.0753 .  
## low_bmi              21.427    128.666   0.167               0.8678    
## ovwt_bmi             92.651     56.411   1.642               0.1012    
## obese_bmi           146.402     59.992   2.440               0.0151 *  
## concep_spring      -206.239     84.598  -2.438               0.0152 *  
## concep_summer      -144.213    106.079  -1.359               0.1747    
## concep_fall         -41.944     99.462  -0.422               0.6735    
## concep_2010         251.274    499.014   0.504               0.6148    
## concep_2011         192.469    500.887   0.384               0.7010    
## concep_2012         462.105    505.747   0.914               0.3614    
## concep_2013         354.254    499.469   0.709               0.4786    
## maternal_age         49.688     27.880   1.782               0.0754 .  
## any_smoker         -180.011     80.822  -2.227               0.0265 *  
## smokeSH             -64.233     54.844  -1.171               0.2422    
## mean_cpss             8.848     27.373   0.323               0.7467    
## mean_epsd           -63.300     27.252  -2.323               0.0207 *  
## male                234.295     46.608   5.027          0.000000736 ***
## mean_o3:mean_temp  -203.061     23.211  -8.748 < 0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 476 on 425 degrees of freedom
## Multiple R-squared:  0.2944, Adjusted R-squared:  0.2512 
## F-statistic: 6.819 on 26 and 425 DF,  p-value: < 0.00000000000000022
plot(bw_lm)
## Warning: not plotting observations with leverage one:
##   1

6 Try a GAM with the ozone and temperature predictor

The NPB model above indicates that there might be a signal for ozone. None of the other exposures had a PIP > 0.5. Here I’ve got a GAM with a smoothing term for ozone and temperature to see about potential nonlinear effects

The mean and standard deviation of the mean_o3 variable are 48.11 (3.14) ppb The mean and standard deviation of the mean_temp variable is 52.67 (4.69) degrees F

library(mgcv)
## Loading required package: nlme
## 
## Attaching package: 'nlme'
## The following object is masked from 'package:dplyr':
## 
##     collapse
## This is mgcv 1.8-34. For overview type 'help("mgcv-package")'.
library(tidymv)

gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)
##  [1] "birth_weight"  "mean_o3"       "mean_temp"     "lat"          
##  [5] "lon"           "lat_lon_int"   "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
#names(gam_df)[2] <- "mean_o3"

head(gam_df)
bw_gam <- gam(birth_weight ~ s(mean_o3, mean_temp) +
                lat + lon + lat_lon_int +
                ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                low_bmi + ovwt_bmi + obese_bmi + 
                concep_spring + concep_summer + concep_fall +
                concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                maternal_age + any_smoker + smokeSH + 
                mean_cpss + mean_epsd + male,
              data = gam_df, method = "REML")
gam.check(bw_gam)

## 
## Method: REML   Optimizer: outer newton
## full convergence after 5 iterations.
## Gradient range [-0.0007907339,0.00003581137]
## (score 3271.262 & scale 200669.8).
## Hessian positive definite, eigenvalue range [4.649398,213.2882].
## Model rank =  53 / 53 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                        k'  edf k-index p-value
## s(mean_o3,mean_temp) 29.0 17.5    0.99    0.41
summary(bw_gam)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int + 
##     ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi + 
##     obese_bmi + concep_spring + concep_summer + concep_fall + 
##     concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age + 
##     any_smoker + smokeSH + mean_cpss + mean_epsd + male
## 
## Parametric coefficients:
##                Estimate Std. Error t value    Pr(>|t|)    
## (Intercept)    2458.848    487.458   5.044 0.000000685 ***
## lat           -6230.541  25040.236  -0.249      0.8036    
## lon            2862.928  11585.059   0.247      0.8049    
## lat_lon_int   -7427.282  29810.771  -0.249      0.8034    
## ed_no_hs        229.723    120.368   1.909      0.0570 .  
## ed_hs           200.488    115.295   1.739      0.0828 .  
## ed_aa           115.944    111.300   1.042      0.2982    
## ed_4yr          172.293    117.681   1.464      0.1439    
## low_bmi          20.693    123.990   0.167      0.8675    
## ovwt_bmi         79.593     54.308   1.466      0.1435    
## obese_bmi       116.811     57.709   2.024      0.0436 *  
## concep_spring  -144.484     93.161  -1.551      0.1217    
## concep_summer  -148.931    133.987  -1.112      0.2670    
## concep_fall     -43.349    127.059  -0.341      0.7331    
## concep_2010     398.744    487.663   0.818      0.4140    
## concep_2011     265.985    490.420   0.542      0.5879    
## concep_2012     634.187    494.055   1.284      0.2000    
## concep_2013     467.863    488.748   0.957      0.3390    
## maternal_age     54.643     26.682   2.048      0.0412 *  
## any_smoker     -199.583     77.274  -2.583      0.0101 *  
## smokeSH         -59.088     52.319  -1.129      0.2594    
## mean_cpss         2.723     26.460   0.103      0.9181    
## mean_epsd       -51.200     26.062  -1.965      0.0501 .  
## male            209.790     44.931   4.669 0.000004102 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                        edf Ref.df    F             p-value    
## s(mean_o3,mean_temp) 17.48  22.45 6.41 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.337   Deviance explained = 39.6%
## -REML = 3271.3  Scale est. = 2.0067e+05  n = 452
save(gam_df, bw_gam, file = here::here("Results", "BW_GAM_v4c.rdata"))
library(mgcViz)
## Loading required package: qgam
## Loading required package: rgl
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
## Registered S3 method overwritten by 'mgcViz':
##   method from  
##   +.gg   GGally
## 
## Attaching package: 'mgcViz'
## The following objects are masked from 'package:stats':
## 
##     qqline, qqnorm, qqplot
gam_b <- getViz(bw_gam)
plot(sm(gam_b, 1)) + 
  l_fitRaster() + l_fitContour() + l_points() +
  labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
  guides(fill=guide_legend(title="Change in\nbirth weight (g)"))

ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_v4c.jpeg"),
       device = "jpeg", width = 5, height = 3, units = "in", dpi = 500)  

7 GAM Sensitivity Analysis

The previous GAM suggested a possible nonlinear relationship between ozone and birth weight. However, this might be the influence of abnormally high and low exposures.

Therefore, Ander suggested a sensitivity analysis where we excluded the top and bottom 2.5% of data and just use the middle 95%.

library(mgcv)

gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)
##  [1] "birth_weight"  "mean_o3"       "mean_temp"     "lat"          
##  [5] "lon"           "lat_lon_int"   "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
head(gam_df)
gam_df2 <- gam_df %>%
  filter(mean_o3 > -2 & mean_o3 < 2) %>%
  filter(mean_temp > -2 & mean_temp < 2)
hist(gam_df2$mean_o3)

hist(gam_df2$mean_temp)

bw_gam2 <- gam(birth_weight ~ s(mean_o3, mean_temp) + 
                lat + lon + lat_lon_int +
                ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                low_bmi + ovwt_bmi + obese_bmi + 
                concep_spring + concep_summer + concep_fall +
                concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                maternal_age + any_smoker + smokeSH + 
                mean_cpss + mean_epsd + male,
              data = gam_df2, method = "REML")
gam.check(bw_gam2)

## 
## Method: REML   Optimizer: outer newton
## full convergence after 5 iterations.
## Gradient range [-0.002508048,0.00007001415]
## (score 3213.214 & scale 200352).
## Hessian positive definite, eigenvalue range [2.617209,209.6741].
## Model rank =  53 / 53 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                        k'  edf k-index p-value
## s(mean_o3,mean_temp) 29.0 13.9    0.98    0.33
summary(bw_gam2)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int + 
##     ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi + 
##     obese_bmi + concep_spring + concep_summer + concep_fall + 
##     concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age + 
##     any_smoker + smokeSH + mean_cpss + mean_epsd + male
## 
## Parametric coefficients:
##                 Estimate Std. Error t value    Pr(>|t|)    
## (Intercept)     2485.535    485.963   5.115 0.000000485 ***
## lat            -8829.102  25156.449  -0.351     0.72579    
## lon             4062.130  11638.673   0.349     0.72725    
## lat_lon_int   -10517.366  29949.212  -0.351     0.72564    
## ed_no_hs         237.733    120.074   1.980     0.04839 *  
## ed_hs            207.494    114.940   1.805     0.07178 .  
## ed_aa            133.082    111.271   1.196     0.23238    
## ed_4yr           172.180    117.485   1.466     0.14354    
## low_bmi           11.100    123.853   0.090     0.92863    
## ovwt_bmi          77.168     54.497   1.416     0.15754    
## obese_bmi        113.451     58.194   1.950     0.05192 .  
## concep_spring   -135.713     92.510  -1.467     0.14315    
## concep_summer   -141.159    131.259  -1.075     0.28282    
## concep_fall      -45.434    124.243  -0.366     0.71479    
## concep_2010      398.176    485.636   0.820     0.41275    
## concep_2011      266.905    488.188   0.547     0.58487    
## concep_2012      609.442    491.975   1.239     0.21615    
## concep_2013      465.282    486.707   0.956     0.33965    
## maternal_age      54.773     26.740   2.048     0.04117 *  
## any_smoker      -214.412     77.843  -2.754     0.00614 ** 
## smokeSH          -62.748     52.606  -1.193     0.23365    
## mean_cpss          1.939     26.609   0.073     0.94193    
## mean_epsd        -49.795     26.136  -1.905     0.05745 .  
## male             201.636     45.062   4.475 0.000009948 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                        edf Ref.df    F   p-value    
## s(mean_o3,mean_temp) 13.92  18.67 3.13 0.0000164 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.235   Deviance explained = 29.8%
## -REML = 3213.2  Scale est. = 2.0035e+05  n = 445
save(gam_df2, bw_gam2, file = here::here("Results", "BW_GAM_Sensitivity_v4c.rdata"))
library(mgcViz)
gam_b2 <- getViz(bw_gam2)
plot(sm(gam_b2, 1)) + 
  l_fitRaster() + l_fitContour() + l_points() +
  labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
  guides(fill=guide_legend(title="Change in\nbirth weight (g)"))

ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_Sensitivity_v4c.jpeg"),
       device = "jpeg", width = 5, height = 3, units = "in", dpi = 500)